Unimodular $f(R,T)$ Gravity

Abstract

We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, are studied. This extension is done in both Jordan and Einstein frames. We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant. Then a general reconstruction method is used to realize an explicit form of the unimodular $f(R,T)$ corresponding to a given cosmological solution. By adopting a specific form of $f(R,T)$, the issue of cosmological inflation is studied in this setup. To see the observational viability of this model, a numerical analysis on the model parameter space is done in the background of Planck2015 observational data.

24 pages, 3 figures, to appear in PRD

References in corpus (72)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Measurements of Omega and Lambda from 42 High-Redshift Supernovae
• Planck 2015 results. XIII. Cosmological parameters
• The Cosmological Constant and Dark Energy
• f(R) Theories Of Gravity
• f(R) theories
• Cosmological Imprint of an Energy Component with General Equation of State
• A Phantom Menace? Cosmological consequences of a dark energy component with super-negative equation of state
• Cosmological Constant - the Weight of the Vacuum
• f(R,T) gravity
• Cosmology and the Fate of Dilatation Symmetry
• A Flat Universe from High-Resolution Maps of the Cosmic Microwave Background Radiation
• Phantom Energy and Cosmic Doomsday
• Disappearing cosmological constant in f(R) gravity
• MAXIMA-1: A Measurement of the Cosmic Microwave Background Anisotropy on angular scales of 10 arcminutes to 5 degrees
• Planck 2013 results. XXII. Constraints on inflation
• Tachyon Matter
• Encyclopaedia Inflationaris
• Extra force in $f(R)$ modified theories of gravity
• Reconstructing the Inflaton Potential --- an Overview
• Formalising the Slow-Roll Approximation in Inflation
• Field Theory of Tachyon Matter
• f(R,L_m) gravity
• The Large Scale Structure of f(R) Gravity
• Can the clustered dark matter and the smooth dark energy arise from the same scalar field ?
• Observational signatures of f(R) dark energy models that satisfy cosmological and local gravity constraints
• Dark Energy Dominance and Cosmic Acceleration in First Order Formalism
• Extended Gravity Theories and the Einstein-Hilbert Action
• Gravity assisted dark energy dominance and cosmic acceleration
• Modified gravity with arbitrary coupling between matter and geometry
• Dynamics of scalar perturbations in f(R,T) gravity
• Dark matter as a geometric effect in f(R) gravity
• Scale invariance, unimodular gravity and dark energy
• The (pseudo)issue of the conformal frame revisited
• On the Trace-Free Einstein Equations as a Viable Alternative to General Relativity
• The Lagrangian description of perfect fluids and modified gravity with an extra force
• Question of quantum equivalence between Jordan frame and Einstein frame
• The quantization of unimodular gravity and the cosmological constant problem
• The matter Lagrangian and the energy-momentum tensor in modified gravity with non-minimal coupling between matter and geometry
• Equivalence of the Einstein and Jordan frames
• A viability criterion for modified gravity with an extra force
• Do f(R) theories matter?
• On the non-minimal gravitational coupling to matter
• Can one tell Einstein's unimodular theory from Einstein's general relativity?
• Cosmological Axion and neutrino mass constraints from Planck 2015 temperature and polarization data
• Unimodular relativity and cosmological constant
• Energy Conditions and Stability in generalized $f(R)$ gravity with arbitrary coupling between matter and geometry
• Unimodular gravity and general relativity from graviton self-interactions
• On unimodular quantum gravity
• The bounce universe history from unimodular $F(R)$ gravity
• Conformal Frame Dependence of Inflation
• On the UV structure of quantum unimodular gravity
• Cosmological Perturbations in Unimodular Gravity
• Inflationary cosmology in unimodular $F(T)$ gravity
• Unimodular $F(R)$ Gravity
• Non-minimally coupled f(R) Cosmology
• Unimodular cosmology and the weight of energy
• Unimodular-Mimetic Cosmology
• Cosmological Implications of Unimodular Gravity
• Unimodular gravity with external sources
• Testing Unimodular Gravity
• Cosmological dynamics of $f(R)$ gravity scalar degree of freedom in Einstein frame
• Cosmological perturbation of Unimodular Gravity and General Relativity are identical
• Non-minimal curvature-matter couplings in modified gravity
• Comparison of Frames: Jordan vs Einstein Frame for a Non-minimal Dark Energy Model
• Tachyon field inflation in the light of BICEP2
• Newton law in covariant unimodular $F(R)$ gravity
• Analyzing modified unimodular gravity via Lagrange multipliers
• Stability analysis of the cosmological solutions with induced gravity and scalar field on the brane
• First Order formulation of Unimodular Gravity
• Dynamics of the universe in the modified unimodular theory of gravity
• Unimodular f(T) gravity

Cited by in corpus (19)

• Teleparallel Gravity: From Theory to Cosmology
• $f(Q,T)$ gravity
• Exploring physical features of anisotropic strange stars beyond standard maximum mass limit in $f\left(R,\mathcal{T}\right)$ gravity
• Palatini formulation of $f(R,T)$ gravity theory, and its cosmological implications
• Generalizing the coupling between geometry and matter: $f(R,L_m,T)$ gravity
• Non-minimal geometry-matter couplings in Weyl-Cartan space-times: $f(R,T,Q,T_m)$ gravity
• Diffusion in unimodular gravity: Analytical solutions, late-time acceleration, and cosmological constraints
• Plane symmetric model in $f(R,T)$ gravity
• Unimodular Einstein--Cartan gravity: Dynamics and conservation laws
• LRS Bianchi I model with constant expansion rate in $f(R,T)$ gravity
• Reheating and particle creation in unimodular f(R, T) gravity
• Nonconservative traceless type gravity
• Warm Inflation in $f(R,T)$ gravity
• Search for the $f(R,T)$ gravity functional form via gaussian processes
• Constrained transit cosmological models in $f(R,L_m,T)$-gravity
• Non-minimal Unimodular Inflation
• Unimodular Theory of Gravity in Light of the Latest Cosmological Data
• Spin effects on particle creation and evaporation in $f(R,T)$ gravity
• Late time cosmological solutions in $f(R,T)$ gravity in a viscous Universe