Emergent Unparticles Dark Energy can restore cosmological concordance

Addressing the discrepancy between the late and early time measurements of the Hubble parameter, H 0, and the so-called S 8 parameter has been a challenge in precision cosmology. Several models are present to address these tensions, but very few of them can do so simultaneously. In the past, we have suggested Banks-Zaks/Unparticles as an emergent Dark Energy model, and claimed that it can ameliorate the Hubble tension. In this work, we test this claim, and perform a likelihood analysis of the model and its parameters given current data, and compare it to ΛCDM. The model offers a possible resolution of Hubble tension and softens the Large Scale Structure (LSS) tension without employing a scalar field or modifying the gravitational sector. Our analysis shows a higher value of H 0 ∼ 70 – 73 km/sec/Mpc and a slightly lower value of S 8 for certain combinations of data sets. Consideration of Planck CMB data combined with the Pantheon sample and SH0ES priors lowers the H 0 and S 8 tension to 0.96σ and 0.94σ respectively with best-fit Δχ 2 ≈ -11 restoring cosmological concordance. Significant improvement in the likelihood persists for other combinations of data sets as well. Evidence for the model is given by inferring one of its parameters to be x 0 ≃ -4.46. The improvement in the fit is driven by the inclusion of the SH0ES prior. In its absence most of the improvement is due to larger error bars in the Emergent Unparticles Dark Energy model.

Nevertheless, the most economical solution -the CC, is still an excellent fit for the data.In arXiv:2302.00067v1[astro-ph.CO] 31 Jan 2023 the past decade, accumulated evidence from various astrophysical probes raises questions on the validity of ΛCDM.While the model is consistent with each probe separately, the best-fit value of cosmological parameters defers by several standard deviations.The reasons may be some unaccounted systematic errors in the different measurements [21], but it may very well be a signal for New Physics [22][23][24][25][26][27][28][29].The tensions we are most interested in are the Hubble tension -which is the most pronounced one, at the level of > 4σ and the S 8 tension [30][31][32][33][34], at the level of 2 − 3σ.Many attempts to reconcile these discrepancies have been put forward [35][36][37][38][39][40][41].However, it seems that many suggestions that reduce the Hubble tension seem to increase the S 8 one [42].
Recently [43][44][45], we have suggested that Dark Energy is due to a Banks-Zaks theory slightly removed from its conformal fixed point and at finite temperature.The theory acts as a perfect fluid.Because the theory is away from the fixed point the energy density and pressure receive a correction that depends on the anomalous dimension and is temperature dependent [46].At high temperatures, the fluid behaves as radiation, and as the temperature decreases with the expansion of the Universe, the correction becomes significant and the fluid behaves as DE and asymptotes to a CC at future infinity.
It is important to note that this behavior is due to the dynamical behavior of the fluid in the FLRW background.Moreover, the DE behavior is not due to some fundamental degree of freedom, but due to the thermodynamical behavior of the fluid.It is an emergent collective macroscopic phenomenon.As such, it is free of initial conditions and fine-tuning problems that are common in the DE literature and has a built-in tracker mechanism.It does not modify gravity and does not include a scalar field with a potential so it is free of the Swampland conjectures [47][48][49].Therefore, it is rather unique compared to other DE models in the literature.In [44,45] we have analyzed the predictions of the model and showed that it is stable.The most notable predictions with respect to ΛCDM are that there is a contribution to N ef f -number of relativistic degrees of freedom at decoupling, and a deviation from w DE = −1 -the equation of state of DE, that may be measured in the future.The model also predicts small deviations from the growth rate of perturbations in ΛCDM, which will be rather difficult to measure.Other interesting constraints can come from its interaction with the CMB [50].Finally, we claimed that the model can ameliorate the Hubble tension.
In this work, we perform a likelihood analysis of our model, dubbed "Emergent Unpar-ticles Dark Energy" (UDE), and derive constraints on the parameters of the model.We consider several data sets -CMB measurements of Planck alone, as well as adding Planck lensing, BAO, DES, and supernovae data -the Pantheon sample and the SH0ES result.
The model provides a significantly better fit to the data compared to ΛCDM, at the level of ∆χ 2 = −2.1-−10.or deviations in the growth of perturbations from the ΛCDM predictions.
The manuscript is organized as follows.We first describe in length the existing Hubble and S 8 tensions.In section III we review the UDE model and its deviation from ΛCDM.
We then list the different data sets that we use in section IV.In V we describe our results.
We then conclude in VI.

II. EXISTING COSMIC TENSIONS
In general, one can consider various tensions or anomalies in cosmological data discussed below.We focus on two celebrated ones -the Hubble tension and the S 8 or Large Scale Structure (LSS) tension.

A. The Hubble (H 0 ) tension
The Hubble tension arises from a discrepancy in the measurements of the present value of the Hubble parameter, H 0 using probes of the early and late Universe.Assuming ΛCDM, the Planck 2018 CMB data infers H 0 = 67.4± 0.5 km/sec/Mpc [1].On the other hand, local direct measurements of SNIa like SH0ES report H 0 = 73.04 ± 1.04 km/sec/Mpc [15] for the ΛCDM Universe.The inferred value of H 0 from CMB is derived from the direct measurements of the angular size of the acoustic scale in the CMB power spectrum while SH0ES measurement is the result of the construction of a cosmic ladder (distance-redshift relation).Currently, there is a ∼ 5 σ discrepancy between these measurements.However, in addition to the aforementioned experiments, the discrepancy in present-day Hubble value (H 0 ) persists even if some other cosmological probe is used to infer the H 0 .For example, one can use the combination of data from Big Bang Nucleosynthesis (BBN), Large Scale Structure data, and Baryonic Acoustic Oscillations measurements resulting in a value of H 0 that is 3.2 − 3.6σ away from SH0ES [51][52][53].
If one assumes that this tension is not due to any experimental systematics, then the measurements are misinterpreted within the ΛCDM model.This fact drives the search for New Physics that resolves the tension.The SH0ES measurement is model-independent, which motivates us to build a model which predicts the increase in the CMB-derived Hubble value to the same as SH0ES.Tons of efforts have been made to increase the value of H 0 .These efforts act in accordance with one of the options to increase the CMB-derived H 0 value: (i) Modification in pre-recombination sound speed, (ii) Modification of the energy density of dark energy before or after recombination, or a combination of both.
The UDE model and its time-dependent equation of state act as a cosmological constant at late times and evolve as radiation at early times, so it belongs to the second type.However, the reduction of the H 0 tension is a byproduct of the UDE model, and not an additional tuning or requirement.We will review the model in the next section.

B. The LSS (S 8 ) tension
In addition to the H 0 tension, data from cosmic shear and galaxy clustering surveys which independently constrain the amplitude of variance in matter fluctuations is quantified as S 8 , Here σ 8 is the measure of the rms amplitude of linear matter density fluctuations over a sphere of radius R = 8M pc/h today, and Ω m is the relative matter-energy density of the Universe today.σ 8 is defined by the following integral: where is P (k) being the linear matter power spectrum calculated today and W (kR) is spherical top-hat filter of radius R = 8 Mpc/h.
There is 2 − 3σ tension between S 8 measured from the data from large-scale structure and Planck CMB data.In particular, CMB derived S 8 comes out to be 0.834 ± 0.016 [1] while Dark Energy Survey measures S 8 = 0.776 ± 0.017 from the combined analysis of the clustering and lensing of foreground and background galaxies respectively [13].Weak lensing surveys such as KiDS report S 8 = 0.759 +0.024 −0.021 [54], and see also [55] that cross-correlate DESI Luminous Red Galaxies and Planck CMB lensing resulting in S 8 = 0.73 ± 0.03.

III. DARK ENERGY FROM UNPARTICLES A. Background Cosmology
We consider the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) Universe filled with unparticles, radiation, and matter with the Friedmann equations, where ρ r and ρ m are the energy density of radiation and matter content of the Universe, that scale as a −4 and a −3 respectively.Unparticles' energy density and pressure are defined as where σ is the "Stefan-Boltzman constant" that measures the number of degrees of freedom, δ = a + γ, a > 0 is a constant which determines the β function around the IR fixed point, γ is an anomalous dimension, y = T Tc is the dimensionless temperature of unparticles and T c , defined in terms of unparticles parameters as , is the temperature of unparticles at which ρ u + p u = 0, [43,44].A unique feature of the model is that the unparticles equation of state is time or temperature dependent.At high temperatures, i.e.
for T Λ U (where Λ U is a cut-off scale of the theory), Banks-Zaks (BZ) particles are coupled to the standard model with energy density ρ = σ BZ T 4 while below the Λ U scale, the BZ sector decouples from SM and the BZ sector is called unparticles. 1 Positive ρ u and T c require authors considered scalar unparticles with a mass as a function of scaling dimension of unparticles.In addition to that Unparticles also have been studied in framework of general relativity and loop quantum cosmology [57,58] where authors discuss the stability of unparticles interacting with radiation.−3 ≤ δ ≤ 0 and B < 0. This particular range of δ ensures that the evolution fulfills the Null Energy Condition.At early times unparticles are in thermal equilibrium with the SM, implying T u ∼ T r , where T u and T r are unparticles and radiation temperature, respectively.
At late times unparticles decouple and asymptote to a CC.This UDE scenario naturally resolves the fine-tuning problem of many DE models.The scenario also exhibits a builtin tracker mechanism [59], in which the energy density of unparticles tracks the radiation throughout the evolution, until it shifts relatively rapidly to a CC-like behavior, making the model immune to initial conditions problem.It is straightforward to write down the temperature (y), energy density (ρ u ) and equation of state (w u ) for unparticles at late-times , y 1 as a function of redshift: The connection between the energy density of DE according to the data [1], ρ c 1.7 × 10 −119 M 4 p , and the parameters of the model is given by: In Fig. 1, we illustrate the parameter space for permissible values of B as a function of δ, which reproduces the current energy density of DE.Considering σ = 100, notice that this energy scale B −1/δ could be in a huge span of energies, 10 −30 M p < B −1/δ < M p .Finally, in Fig. 2, we illustrate the evolution of the ratio of the energy density of unparticles to the energy density of the radiation content of the Universe (left panel) and the evolution of the ratio of the Hubble parameter UDE and ΛCDM cosmologies given the same initial value at z = 0 in the right panel.The initial value has been taken as the ΛCDM one from Table II, H 0 = 67.3 and the increase in the Hubble parameter as a function of redshift by a few percent in UDE is obvious.

B. Perturbations
Next, we move to the evolution of perturbations in the presence of unparticles.Perturbations to the FLRW background give rise to CMB and the structure that we see today.We study the evolution of linear perturbations using the publicly available Einstein-Boltzmann equation solver code CAMB [60].We modify the CAMB dark energy module in order to study the evolution of background and perturbation.We use the perfect fluid prescription of unparticles.In a spatially flat universe, the evolution of the density contrast δ u and the fluid velocity θ u of unparticles are governed by the following equations [61].
where δpu δρu is the adiabatic sound speed and Φ is the gravitational potential.These equations are solved numerically while assuming adiabatic initial conditions.
Hence, we can analyze the effect of UDE on CMB and matter power spectra.In Fig (3) we show the CMB temperature spectrum We then investigate the UDE affecting observables beyond the CMB temperature and polarization power spectra.The left panel of Fig 4 shows the increase in the nonlinear matter power spectrum as a result of a decrease in unparticles' temperature.The right panel again shows the departure of the matter power spectrum of the UDE scenario with respect to ΛCDM.We see the oscillatory departure from the ΛCDM at small scales.

IV. DATA
The inferred values of the cosmological parameters have certain dependence on the data sets used.Different combinations of data sets will result in somewhat different values.We use various data sets to constrain the UDE model and compare the results to ΛCDM.We modify the publicly available Einstein-Boltzmann code CAMB [60] in conjunction with Cobaya [65] to perform the Markov-Chain Monte Carlo (MCMC) simulations.In our analysis, we use the following publicly available data sets: • Planck 2018 CMB : First, we consider the Planck 2018 likelihood for the CMB data, which consists of the low-l TT, low-l EE, and high-l TTEETE power spectra [2].We also use the Planck 2018 lensing likelihood [3], which has an important role in the LSS analysis of the Late Universe.• Baryon Acoustic Oscillations (BAO) and RSD measurements: We use the measurements from the SDSS DR7 Main Galaxy Sample (MGS) [4] and 6dF galaxy survey [5] measurements at z = 0.15 and z = 0.106 respectively.In addition to that, we also include BAO and f σ 8 measurements (where f is the linear growth rate) from BOSS DR12 & 16 at z = 0.38, 0.51, 0.68 [6][7][8][9], QSO measurements at z = 1.48 [10,11] and Ly-α auto-correlation and cross-correlation with QSO at z = 2.2334 [12].
• Supernovae Pantheon: The Pantheon data set is a collection of the absolute magnitude of 1048 supernovae distributed in redshift interval 0.01 < z < 2.26 [14].Many times we will simply refer to this data set as SN.
• H 0 from SH0ES: We use latest local measurement of H 0 = 73.04 ± 1.4km/sec/Mpc from the SH0ES team [66].Many times we will simply refer to this data set as H 0 .

A. Priors
Let us compare the cosmological parameter constraints on UDE and ΛCDM.We fit the different data sets described in the previous section alone or several of them combined together.We fix the parameter δ = −3 because it allows quick implementation of the model in CAMB.However, we have verified that any value of δ lying in the range [−3, 0] will not considerably affect the cosmological observables using compressed likelihoods [67].The other free parameter of the UDE model is the present value of unparticles dimensionless temperature y 0 , which we set free.For numerical implementation, we parameterize y 0 as 1 + 10 x 0 where y 0 = 1 shows the temperature of unparticles at future infinity and adopt a uniform prior x 0 ∈ [−4.5, −3].Except for x 0 we constrain the other standard cosmological parameters for both cosmologies -the baryon matter density Ω b h 2 , the cold dark matter density Ω c h 2 , the amplitude of primordial curvature spectrum amplitude A s evaluated at suitable pivot scale, k = 0.05M pc −1 along with its tilt n s , and the reionization optical depth τ reio .We use the standard three neutrino description with one massive with mass, m ν = 0.06 eV, and two massless neutrinos.Table I lists the priors for different parameters for all cosmologies described above.In each subsection, we explain the reasons for choosing the particular combination of data sets.
B. Results

Primary Planck 2018
We first consider the Planck 2018 primary CMB TT, TE, and EE power spectrum data, as it is one of the main drivers of the tension.We have analyzed the Pantheon data only in [45].The constraints on cosmological parameters at 1-σ CL are tabulated in Table II     We now expand our analysis to include the DES-Y1 data set.We jointly analyze Planck 2018 CMB, Lensing, BAO and Pantheon data along with DES-Y1 as to compare with the SH0ES data that is responsible for the H 0 tension with other probes.We implement the Halofit formula [68] to account for the non-linear matter clustering, which is important to model galaxy-galaxy weak lensing correlation functions.The posterior distributions for our  We find H 0 = 70.22+0.49−0.66 , S 8 = 0.810 +0.011 −0.0080 and Ω m = 0.2985 +0.0054 −0.0044 for the UDE scenario.This brings down the H 0 and S 8 tensions to around 1.87σ and 1.3σ with SH0ES and DES Y1 respectively for UDE model.For ΛCDM, we find H 0 = 68.22 ± 0.36 , S 8 = 0.812 ± 0.0093 and Ω m = 0.3037 ± 0.0047 which are in 3.30σ and 1.41σ tension.The χ 2 statistics for each data set in this fit are presented in table IV.The UDE improvement in the total χ 2 -statistic is ∆χ 2 = +0.77which is not a better fit with one additional parameter, x 0 .

Planck 2018 Lensing+BAO+DES+SN+H0
Next, we combine the data sets which are classified as low redshift (late time measurements), i.e. without Primary Planck 2018, which is driving both tensions.We point out that with this compilation, we get the highest value of the Hubble parameter, close to the SH0ES-only measurement.The posterior distributions are shown in Fig 8, and parameter constraints are in Table V.The UDE model is favored by the data sets as there is ∆ χ 2 = −2.1 with respect to ΛCDM.For the UDE scenario, we find H 0 to be 72.9 ± 1.4, which is 1.63 σ away from Planck only derived Hubble constant in Table II.We find that S 8 = 0.790 ± 0.018 which has almost 1.01σ discrepancy from the Planck 2018 value.

Primary Planck 2018+SN+H 0
We now jointly fit Primary Planck 2018, SN, and H 0 as to avoid the inclusion of f σ 8 measurements in BAO measurements.We find H 0 = 68  VI.The UDE scenario is most favored by this particular combination of data with ∆χ total = −10.36.Again the improvement in the likelihood is mostly driven by the fit to the SH0ES data.This is the best improvement in the likelihood we have achieved and both tensions are reduced to less than one standard deviation.in ΛCDM and S 8 = 0.808 +0.010 −0.0078 compared to 0.8111 +0.0080 −0.015 for ΛCDM.The resulting tensions in H 0 and S 8 with respect to SHOES and DES-Y1 are 1.66 σ and 1.25σ respectively.The best-fit value for the unparticles parameter x 0 = −4.380+0.038 −0.12 and there is a significant improvement in the likelihood of ∆χ 2 = −7.72.

VI. CONCLUSIONS
We have discussed the possibility of unparticles as viable Dark Energy candidate, in the UDE model.As the Banks-Zaks theory is displaced from its conformal fixed point, the energy density and pressure of the fluid have two terms resulting in a temperaturedependent equation of state.As a result, along with the dynamics of the Universe, the fluid has a limiting temperature, which causes unparticles to evolve as a radiation-like fluid and asymptote to a CC in early and late times, respectively.The consideration of unparticles as a DE source makes the theory immune to cosmic coincidence and no-dS conjecture.A major point is the fact that the DE behavior is emergent -due to the thermodynamical behavior of the fluid, and not because of some specific degree of freedom in vacuum or a modification of gravity.We further investigated the challenges posed by Hubble (H 0 ) and large-scale structure S 8 tension in the era of precision cosmology.In this work, we analyzed the suggestion that the UDE scenario accounts for the discrepancy between various data sets.We find that the UDE scenario can alleviate both tensions.We also find evidence of obtaining the Unparticles in the Universe, such that x 0 −4.3, or more conservatively −5 < x 0 < −4.
To quantify the evidence of UDE, we have shown the effect of UDE parameter x 0 on the  To summarize, the model is restoring the cosmological concordance.
It would be interesting to further test the UDE model.This can proceed in several ways.First, since the UDE behaves as radiation at early times, at a certain point such extra radiation should appear in the form of ∆N ef f. , which should be measured (consistent with the value of x 0 ).Second, going to higher redshifts in galaxy surveys and weak lensing experiments up to z ∼ 5 will allow us to measure the time dependence of the equation of state parameter w(z) thus confirming or ruling out the model.These measurements will also improve the measurement of the growth factor f where there is also some difference between ΛCDM and UDE [44].Third, considering the effect of UDE on ISW at early and late times [62][63][64].Fourth, evaluating carefully the effects suppressed couplings between the Banks-Zaks theory and the Standard Model may have.A first interesting attempt has been carried out in [50].Fifth, going beyond the fluid approximation one may consider microscopic effects that can be observed.Sixth, one would like better theoretical control of the model, where δ can be derived, rather than being a free parameter.
The "problem" of UDE until now has been that the deviations may be so small compared to ΛCDM that they will not be detectable.The present work shows that at least part of the parameter space of the model, with −5 < x 0 < −4 is favorable since it considerably reduces existing cosmological tensions and is a statistically significant better fit to the data.Going beyond the specific model, we can try and learn some general lessons for model building for treating the Hubble and LSS tension.It seems an important feature is the change in the equation of state w(z) from radiation to DE.It would be interesting to consider other models that exhibit such behavior and better yet analyzing such a phenomenon in a modelindependent way which we plan to do next.

ρ c = 1 . 7 × 10 -119 M p 4 - 3 ρ c = 1 . 7 × 10 -119 M p 4 FIG. 1 :
FIG. 1: Left panel: The dependence of B on δ such that the energy density of unparticles accounts for the energy density of DE today Ω DE,0 .Right panel: A comparison of B with respect to the Planck scale.B has dimensions of M −δ p .Note that δ ∼ −0.068 one obtains B is equal to the Planck scale.In all cases, we take σ = 100.

FIG. 2 :
FIG. 2: Left panel: Ratio of unparticles energy density to the radiation energy density for different values of x 0 ∈ [−5.0, −4.0],where y 0 = 1 + 10 x 0 .Right panel: The ratio between the Hubble parameter in UDE to that of ΛCDM as a function of redshift.Both plots show the different background behavior of the UDE model as a function of redshift.We have used the best-fit values for the cosmological parameters for Planck 2018 for both models given in Table II in these plots.
for different values of x 0 and the fractional change ∆D T T .We choose the best-fit values of cosmological parameters from the Planck 2018 derived for both models.It is clear from the left panel in Fig 3 that a decrease in the present temperature of unparticles leads to suppression in peaks of D T T l while the right panel shows the amplification in D T T l for ∈ (10 − 1000) and oscillations in residual of D T T l for large > 10 3 .It will be interesting to understand these amplifications and oscillations as late or early-time integrated Sachs-Wolfe (ISW) signals [62-64].

FIG. 3 :
FIG. 3: Left Panel: Plot of CMB temperature anisotropy power spectra for different x 0 .The peaks of the temperature spectrum D T T are suppressed as we decrease x 0 .Right Panel: Residuals ∆D T T for UDE with respect to ΛCDM using the best fit values of H 0 = 69.99km/sec/Mpc and H 0 = 67.3km/sec/Mpc, respectively.

FIG. 4 :
FIG.4: Left Panel: The Non-linear (solid) and linear (dashed) matter power spectrum P (k) at z = 0 for the UDE model that fits the primary CMB data.The amplitude of P (k) in the range 0.1 h/Mpc ≤ k ≤ 1h/ Mpc decreases for higher temperature of unparticles today.Right panel: Ratio of UDE and ΛCDM non-linear matter power spectra at z = 0.The model parameters are the same as in the previous figures.The suppression in the amplitude of P (k) has a significant role in the change of σ 8 and hence S 8 .This decrease in S 8 is the result of shifts in standard cosmological parameters in the UDE model.

FIG. 8 :
FIG. 8: Posterior distribution of cosmological parameters from Lensing+BAO+DES+SN+H 0 data.We present the contour plots for ΛCDM and UDE in blue and red respectively with 1σ and 2σ CL.

6 .
Primary Planck 2018+Lensing+BAO+SN+DES+H 0 Finally, we combine all data -Primary Planck 2018, Planck 2018 CMB lensing, BAO, DES, Pantheon, and SH0ES data.The Posterior distributions for this combination of data sets are shown in Fig 10.The best-fit parameters and 68% CL constraints on cosmological parameters are tabulated in Table VII.We find H 0 = 70.87+0.61 −0.79 compared to H 0 = 68.28+0.71 −0.31

FIG. 12 :
FIG. 12: The 2-D marginalized PDF contours for H 0 − S 8 and Ω m − S 8 in left and right panel respectively.We compare the alleviated H 0 and S 8 tensions in the UDE scenario with respect to SHOES and DES within ΛCDM.The SHOES and DES measurements are represented in Gray.The Unparticles results are shown in green and red for CMB Planck 2018 and All data sets respectively while Planck ΛCDM is denoted in blue.In fig, base means the combination of CMB Planck 2018 + BAO + SN measurements.
4. Most importantly, it reduces the Hubble tension with H 0 70 km/s/Mpc in accord with supernovae type Ia (SNIa) measurements and slightly reduces the S 8 tension to S 8 0.78 − 0.816.Hence, we have an economical model that relieves existing tensions without introducing new ingredients and is based on collective phenomena.Future cosmological observations can further test the UDE model by measuring N ef f , w DE

TABLE I :
Priors used on various free parameters of ΛCDM and Unparticles model* for MCMC . We find a bound on x 0 < −4.40 at 68 % CL.A comparison of the posterior distributions in UDE and ΛCDM is presented in Fig 5. We find the Hubble constant in UDE to be H 0 = 69.99+0.84−1.1km/sec/Mpc, shifted upwards compared to ΛCDM for the same data, H 0 = 67.30± 0.65 km/sec/Mpc with slightly larger error bars.We also find S 8 = 0.819±0.021with significantly lower value than the ΛCDM value S 8 = 0.833 ± 0.017.However, this value of S 8 is still larger than the DES-only result.The possible reason for reducing the Planck derived S 8 value towards the lower S 8 from DES is the reduction of total matter density (Ω m ) to 0.303 ± 0.011 in UDE from the ΛCDM scenario Ω m = 0.3162 ± 0.008 while keeping the σ 8 value almost same.

TABLE II :
The mean ±1σ(best-fit) constraints on the cosmological parameters inferred from the Planck 2018 CMB data only (TTEETE) for ΛCDM and UDE scenario.The constraints are reported at the 68 % CL.We also report the χ 2 min for each model and data sets.We find that H 0 and S 8 are reduced to 1.7σ and 1.37σ with SH0ES and DES measurements respectively.We find an upper bound on unparticles temperature today x 0 < −4.40.Mpc reducing the H 0 tension with SH0ES to ≈ 1.39 σ from the H 0 = 68.09+0.63 −0.41 inferred from ΛCDM which is in 3.19σ tension with the SH0ES result.
measurement is in tension with Planck.The Posterior distributions for this combination of data sets are shown in Fig 6.The best-fit parameters and 68% CL constraints on cosmological parameters are tabulated in Table III.We find H 0 = 70.69+0.60 −0.89 km/sec/Considering the LSS tension, there is little difference as the value of S 8 is brought down with S 8 = 0.816 +0.011 −0.008 for UDE compared to S 8 = 0.818 +0.010 −0.015 for ΛCDM.We find x 0 =

TABLE IV :
The mean ±1σ(best-fit) constraints on the cosmological parameters inferred from the , including the full DES Y1 likelihood, are shown in Fig 7. Parameter constraints with χ 2 values are tabulated in TableIV.We report that the inclusion of the DES Y1 does not show significant evidence for UDE.The data sets put a bound on x 0 < −4.42. analysis

TABLE V :
The mean ±1σ(best-fit) constraints on the cosmological parameters inferred from the Planck 2018 CMB lensing, Baryon Acoustic Oscillations data from various surveys, Pantheon SNIa redshift-luminosity data, Dark Energy Survey-Y1 and local measurements for H 0 by SH0ES team for ΛCDM, and UDE.Notice the higher value of H 0 and lower value of S 8 .

TABLE VI :
The mean ±1σ(best-fit) constraints on the cosmological parameters inferred from the Planck 2018 CMB data ( TTEETE), Pantheon SNIa redshift-luminosity data and local measurements for H 0 by SH0ES team for ΛCDM and UDE.
Posterior distribution of cosmological parameters from the Primary Planck 2018 + SN + H 0 .We present the contour plots for ΛCDM and UDE in blue and red respectively with 1σ and 2σ CL.Notice the notable difference in the preferred values of H 0 and S 8 .

TABLE VII :
The mean ±1σ(best-fit) constraints on the cosmological parameters inferred from the Planck 2018 TTEETE , Planck 2018 CMB lensing, BAO, Pantheon, Dark Energy Survey -Y1 and H 0 by SH0ES team for ΛCDM and UDE.