Observational constraints to a phenomenological $f\left(R,\nabla R\right)$-model

Abstract

This paper analyses the cosmological consequences of a modified theory of gravity whose action integral is built from a linear combination of the Ricci scalar $R$ and a quadratic term in the covariant derivative of $R$. The resulting Friedmann equations are of the fifth-order in the Hubble function. These equations are solved numerically for a flat space section geometry and pressureless matter. The cosmological parameters of the higher-order model are fit using SN Ia data and X-ray gas mass fraction in galaxy clusters. The best-fit present-day $t_0$ values for the deceleration parameter, jerk and snap are given. The coupling constant $\beta$\ of the model is not univocally determined by the data fit, but partially constrained by it. Density parameter ${\Omega }_{m0}$ is also determined and shows weak correlation with the other parameters. The model allows for two possible future scenarios: there may be either a premature Big Rip or a Rebouncing event depending on the set of values in the space of parameters. The analysis towards the past performed with the best-fit parameters shows that the model is not able to accommodate a matter-dominated stage required to the formation of structure.

18 pages, 7 figures. References added, email and typos corrected. No major change. Celebrating the 70th birthday of Prof. Mario Novello

References in corpus (18)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Extended Theories of Gravity
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• New Hubble Space Telescope Discoveries of Type Ia Supernovae at z > 1: Narrowing Constraints on the Early Behavior of Dark Energy
• The Hubble Space Telescope Cluster Supernova Survey: V. Improving the Dark Energy Constraints Above z>1 and Building an Early-Type-Hosted Supernova Sample
• A 3% Solution: Determination of the Hubble Constant with the Hubble Space Telescope and Wide Field Camera 3
• Spectra and Light Curves of Six Type Ia Supernovae at 0.511 < z < 1.12 and the Union2 Compilation
• Dark torsion as the cosmic speed-up
• Einstein's Other Gravity and the Acceleration of the Universe
• Observational Constraints on the Nature of the Dark Energy: First Cosmological Results from the ESSENCE Supernova Survey
• Consequences of dark matter-dark energy interaction on cosmological parameters derived from SNIa data
• Backreaction in late-time cosmology
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Exact solution to the averaging problem in cosmology
• Stable bounce and inflation in non-local higher derivative cosmology
• Backreaction: directions of progress
• Modified Friedmann model in Randers-Finsler space of approximate Berwald type as a possible alternative to dark energy hypothesis
• Realistic Cyclic Magnetic Universe

Cited by in corpus (11)

• On higher derivative corrections to the $R+R^2$ inflationary model
• Cosmology of $f(R,\square R)$ gravity
• Novel higher-curvature variations of $R^2$ inflation
• Scalar-multi-tensorial equivalence for higher order $f\left(R,{\nabla }_{\mu }R,{\nabla }_{{\mu }_1}{\nabla }_{{\mu }_2}R,...,{\nabla }_{{\mu }_1}...{\nabla }_{{\mu }_n}R\right)$ theories of gravity
• Dynamical analysis of the covarying coupling constants in scalar-tensor gravity
• $f\left(R,{\nabla }_{{\mu }_1}R,\dots ,{\nabla }_{{\mu }_1}\dots {\nabla }_{{\mu }_n}R\right)$ theories of gravity in Einstein frame: A higher order modified Starobinsky inflation model in the Palatini approach
• Observational constraints on varying fundamental constants in a minimal CPC model
• Gravitational waves in higher-order $R^2$ gravity
• Alternative approach to the Starobinsky model for inflation scenarios
• Black holes and wormholes in $f(R)$ gravity with a kinetic curvature scalar
• Reconstruction of DBI-essence dark energy with f(R) gravity and its effect on black hole and wormhole mass accretion