Spatial Curvature in $f(R)$ Gravity

Abstract

In this work, we consider four $f(R)$ gravity models -- the Hu-Sawicki, Starobinsky, Exponential and Tsujikawa models -- and use a range of cosmological data, together with Markov Chain Monte Carlo sampling techniques, to constrain the associated model parameters. Our main aim is to compare the results we get when ${\Omega }_{k,0}$ is treated as a free parameter with their counterparts in a spatially flat scenario. The bounds we obtain for ${\Omega }_{k,0}$ in the former case are compatible with a flat geometry. It appears, however, that a higher value of the Hubble constant $H_0$ allows for more curvature. Indeed, upon including in our analysis a Gaussian likelihood constructed from the local measurement of $H_0$, we find that the results favor an open universe at a little over $1\sigma$. This is perhaps not statistically significant, but it underlines the important implications of the Hubble tension for the assumptions commonly made about spatial curvature. We note that the late-time deviation of the Hubble parameter from its $\Lambda$CDM equivalent is comparable across all four models, especially in the non-flat case. When ${\Omega }_{k,0}=0$, the Hu-Sawicki model admits a smaller mean value for ${\Omega }_{\text{cdm},0}{h}^2$, which increases the said deviation at redshifts higher than unity. We also study the effect of a change in scale by evaluating the growth rate at two different wavenumbers $k_{†}$. Any changes are, on the whole, negligible, although a smaller $k_{†}$ does result in a slightly larger average value for the deviation parameter $b$.

arXiv comment21 pages, 11 figures, 8 tables

References in corpus (84)

• Planck 2015 results. XIII. Cosmological parameters
• f(R) Theories Of Gravity
• f(R) theories
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample
• The Complete Light-curve Sample of Spectroscopically Confirmed Type Ia Supernovae from Pan-STARRS1 and Cosmological Constraints from The Combined Pantheon Sample
• The 6dF Galaxy Survey: Baryon Acoustic Oscillations and the Local Hubble Constant
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results
• The Cosmic Linear Anisotropy Solving System (CLASS) II: Approximation schemes
• Is Cosmic Speed-Up Due to New Gravitational Physics?
• Baryonic Features in the Matter Transfer Function
• Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• The Clustering of the SDSS DR7 Main Galaxy Sample I: A 4 per cent Distance Measure at z=0.15
• Cosmological Perturbation Theory in the Synchronous vs. Conformal Newtonian Gauge
• Cosmological Perturbation Theory in the Synchronous and Conformal Newtonian Gauges
• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Chameleon Fields: Awaiting Surprises for Tests of Gravity in Space
• Disappearing cosmological constant in f(R) gravity
• Constraints on the redshift dependence of the dark energy potential
• A 6% measurement of the Hubble parameter at $z\sim 0.45$: direct evidence of the epoch of cosmic re-acceleration
• Cosmic Chronometers: Constraining the Equation of State of Dark Energy. I: H(z) Measurements
• Raising the bar: new constraints on the Hubble parameter with cosmic chronometers at z$\sim$2
• Improved constraints on the expansion rate of the Universe up to z~1.1 from the spectroscopic evolution of cosmic chronometers
• Constraining Cosmological Parameters Based on Relative Galaxy Ages
• The WiggleZ Dark Energy Survey: Joint measurements of the expansion and growth history at z < 1
• Class of viable modified $f(R)$ gravities describing inflation and the onset of accelerated expansion
• Conservative Constraints on Early Cosmology: an illustration of the Monte Python cosmological parameter inference code
• Can modified gravity explain accelerated cosmic expansion?
• Conditions for the cosmological viability of f(R) dark energy models
• 1/R gravity and Scalar-Tensor Gravity
• Age-dating Luminous Red Galaxies observed with the Southern African Large Telescope
• Do consistent $F(R)$ models mimic General Relativity plus $\Lambda$?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Measurement of BAO correlations at $z=2.3$ with SDSS DR12 \lya-Forests
• Scalar-tensor gravity in an accelerating universe
• Quintessence without scalar fields
• An Open Universe from Inflation
• f(R) Gravity and Chameleon Theories
• A Lower Growth Rate from Recent Redshift Space Distortion Measurements than Expected from Planck
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• Baryon acoustic oscillations from the complete SDSS-III Ly$\alpha$-quasar cross-correlation function at $z=2.4$
• The Subaru FMOS galaxy redshift survey (FastSound). IV. New constraint on gravity theory from redshift space distortions at $z\sim 1.4$
• Matter instability in modified gravity
• Evolution of the $f{\sigma }_8$ tension with the Planck15/$\Lambda$CDM determination and implications for modified gravity theories
• The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights
• Exponential Gravity
• Eppur è piatto? The cosmic chronometer take on spatial curvature and cosmic concordance
• The VIMOS Public Extragalactic Redshift Survey (VIPERS): The growth of structures at $0.5<z<1.2$ from redshift-space distortions in the clustering of the PDR-2 final sample
• Fourth order gravity: equations, history, and applications to cosmology
• Dynamical Dark Energy or Simply Cosmic Curvature?
• The growth rate of cosmic structure from peculiar velocities at low and high redshifts
• Observational constraints on Galileon cosmology
• On the evolution of density perturbations in f(R) theories of gravity
• Cosmological parameter constraints from SDSS luminous red galaxies: a new treatment of large-scale clustering
• The galaxy power spectrum take on spatial curvature and cosmic concordance
• Autonomous Dynamical System Approach for $f(R)$ Gravity
• Density perturbations in f(R) gravity theories in metric and Palatini formalisms
• Gauge-ready formulation of the cosmological kinetic theory in generalized gravity theories
• New observational constraints on $f(R)$ gravity from cosmic chronometers
• Observational constraints on viable f(R) parametrizations with geometrical and dynamical probes
• A Toy Model for Open Inflation
• Can we have inflation with Omega > 1?
• Some remarks on the dynamical systems approach to fourth order gravity
• Cosmic history of viable exponential gravity: Equation of state oscillations and growth index from inflation to dark energy era
• Internal Robustness of Growth Rate data
• Is exponential gravity a viable description for the whole cosmological history?
• Unraveling the effective fluid approach for $f(R)$ models in the subhorizon approximation
• Emerging spatial curvature can resolve the tension between high-redshift CMB and low-redshift distance ladder measurements of the Hubble constant
• f(R) gravity: successes and challenges
• Theoretical and observational constraints of viable f(R) theories of gravity
• Inflation in a closed universe
• Testing Hu-Sawicki f(R) gravity with the Effective Field Theory approach
• Cosmological constraints and comparison of viable $f(R)$ models
• Cosmological dynamics of fourth order gravity: A compact view
• Relativistic numerical cosmology with Silent Universes
• Spatial curvature endgame: Reaching the limit of curvature determination
• Distance Priors from \emph{Planck} 2015 data
• Cosmological constraints on the Hu-Sawicki modified gravity scenario
• The most general fourth order theory of Gravity at low energy
• Matter Power Spectra in Viable $f(R)$ Gravity Models with Massive Neutrinos
• Using spatial curvature with HII galaxies and cosmic chronometers to explore the tension in $H_0$
• What if Planck's Universe isn't flat?
• On the perturbation theory in spatially closed background
• Cosmological Perturbations and Quasi-Static Assumption in $f(R)$ Theories

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