ON THE COSMIC ACCELERATION AND MATTER CLUSTERING IN MODIFIED f(R) GRAVITY MODELS

Abstract

itulo original da tese: ON THE COSMIC ACCELERATION AND MATTER CLUSTERING IN MODIFIED f(R) GRAVITY MODELS Understanding the origin of the current accelerated expansion of the universe is one of the greatest challenges in modern cosmology and particle physics. In the context of the standard cosmological model, the ΛCDM model, this acceleration is attributed to the cosmological constant Λ, or, equivalently, to the energy density of the quantum vacuum, which is recognized as the simplest form of dark energy. It turns out that, whether through a cosmological constant or more general forms of dark energy, this explanation for the origin of recent cosmic acceleration has some internal shortcomings. On the one hand, within the standard view of cosmology, two issues involving the cosmological constant concern both particle physicists and cosmologists: (i) the vacuum energy density measured via cosmological observations is astoundingly smaller than that estimated by quantum field theory (up to 120 orders of magnitude, depending on the theory used); and (ii) the normalized vacuum and matter energy densities have curiously close values today, which appears to be a cosmic coincidence. On the other hand, it should be possible to observe dark energy directly, since it corresponds to approximately 70% of the total energy density of the universe according to current observations. However, no dark energy has been observed directly at a fundamental level (in particle physics) to date. All evidence of an energetic component exerting negative pressure on the universe comes from indirect cosmological observations. In order to avoid the issues inherent to a cosmological constant, or to more general forms of dark energy, some alternative scenarios based on a suitable modification of General Relativity, the current theory of gravity, have been proposed. This is the case with the f(R) theories of gravity, which generalize gravitation by replacing the term R − 2Λ in the Einstein-Hilbert Lagrangian by a general function of the Ricci scalar, R. These theories are known to properly explain cosmic acceleration as an effect of the spacetime geometry, instead of an exotic form of dark energy. They are also conformally equivalent to Einstein’s theory with the addition of an extra degree of freedom in the gravitational sector, the scalaron, a canonical scalar field whose potential is uniquely determined by the Ricci scalar curvature, R. In this thesis, we study the cosmological viability of three f(R) models, namely, the Appleby-Battye, Hu-Sawicki, and Starobinsky models. We first derive the equations of motion for each model and numerically solve them for important parameters of the cosmological background: the Hubble rate H(z) and the equation of state wDE(z). Since the cosmological background is highly degenerate, we proceed to the perturbative level by numerically solving the differential equations related to the matter density contrast δm(z) and the normalized growth rate at the physical scale of 8Mpc/h, [fσ8](z), for each model. Next, we perform MCMC statistical analyses and constrain the free parameters of the Appleby-Battye and Hu-Sawicki models by considering three cosmological datasets: H(z) measurements from the cosmic chronometer method, [fσ8](z) from redshift-space distortion observations, and type Ia supernovae mB(z) measurements from Pantheon+ and SH0ES collaborations. Our results are consistent with those reported in the literature for the cosmological parameters, such as the Hubble constant (H0), the normalized matter density (Ωm,0), the variance of matter fluctuations at the scale of 8Mpc/h (σ8,0), and the absolute magnitude (MB), in both cases. Additionally, our best-fit model parameters were: b = 2.28 +6.52 −0.55 (SNe Ia data alone) and b = 2.18 +5.41 −0.55 (SNe+CC+RSD data combination), encompassing General Relativity (b ≫ 1) at 2σ CL, for the Appleby-Battye model, and μ = 77.0 +18.0 −56.0 (SNe Ia data alone) and μ = 93.0 +41.0 −55.0 (SNe+CC+RSD data combination), which excludes General Relativity (μ = 0) at 2σ CL, for the Hu-Sawicki model. Finally, the Akaike information criterion penalized both the Appleby-Battye and Hu-Sawicki models due to each having an additional independent parameter compared to the flat-ΛCDM reference model: ∆AIC = 0.716 and ∆AIC = 132.969, respectively. However, our results show that the Appleby-Battye model exhibits an AIC value very close to that of the flat-ΛCDM model (∆AIC ∼ 0.7), making it a competitive alternative to the standard model in describing the accelerated expansion and growth of structures in the universe, but without requiring any exotic dark energy.