Testing logarithmic corrections to R2 -exponential gravity by observational data

Abstract

Tver state university 170002, Sadovyj per. 35, Tver, Russia This paper is devoted to the analysis of a class of F (R) gravity, where additional logarithmic corrections are assumed. The gravitational action includes an exponential term and a R 2 inflationary term, both with logarithmic corrections. This model can unify an early time inflationary era and also the late time acceleration of the universe expansion. This model is deeply analysed, confronting with recent observational data coming from the largest Pantheon Type Ia supernovae sample, the latest measurements of the Hubble parameter H(z), manifestations of Baryon Acoustic Oscillations and Cosmic Microwave Background radiation. The viability of the model is studied and the corresponding constraints on the free parameters are obtained, leading to an statistical analysis in comparison to ΛCDM model. The inflationary era is also analysed within this model and its compatibility with the latest observational data for the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio. Finally, possible corrections on the Newton's law and constraints due to primordial nucleosynthesis are analysed.

Testing the equation of state for viscous dark energy

“…The CMB observations (26) with small errors σ i (27) produce the most strict limitations in the parameter space in comparison with other data. For that reason, we analyse separately the χ 2 function obtained after fitting the free parameters with SNe Ia, BAO and H(z) data at redshifts 0 < z ≤ 2.36 [18,19]:…”

“…Here C SN is the 1048 × 1048 covariance matrix [22]. For any set of the model parameters (16) we solve the system of equations provided in (13) and (14), obtaining the Hubble parameter H(z), and consequently the luminosity distances (19) and the distance moduli (18). We also marginalise the χ 2 SN function over the nuisance parameter H 0 [18][19][20][21].…”

“…As in previous works (see Refs. [18,19]), here we use 17 BAO data points for d z (z) and 7 data points for A(z) from Refs. [31] estimated for galaxy clusters with mean redshifts z = z i and represented in Table I.…”

“…The covariance matrix C CMB = C ij σ i σ j , C 12 = 0.53,C 13 = −0.73,C 23 = −0.42 and other details are described in [34] and also in Refs. [18,19].…”

“…In that sense, we study a model whose viscosity depends on the powers of the energy density and the Hubble parameter, being considered as effective corrections to a perfect dark energy fluid, while the second model is inspired in Anton-Schmidt's equation of state for crystalline solids ( [17]). We test the model by using some recent observational data, and techniques developed in some previous papers [18][19][20][21]. The observational datasets include the latest Pantheon sample [22] of Type Ia supernovae (SNe Ia), estimations of the Hubble parameter H(z), observational manifestations of baryon acoustic oscillations (BAO) and cosmic microwave background radiation (CMB) [23][24][25][26].…”