FLRW solutions in $f(Q)$ theory: the effect of using different connections

Abstract

We study a Friedmann-Lema\^ıtre-Robertson-Walker (FLRW) space-time in the theory of $f(Q)$-gravity, where $Q$ denotes the non-metricity scalar. It has been previously shown in the literature, that there exist four distinct families of connections, which are compatible with the isometries of the FLRW metric; three for the spatially flat case and one when the spatial curvature is present. In the spatially flat case, one connection is dynamically irrelevant and yields the dynamics of the coincident gauge in the Cartesian coordinates. For this, we obtain the general solution of an arbitrary $f(Q)$ theory with a perfect fluid matter content, and present various examples for specific choices of the $f(Q)$ function. We proceed by studying the effect of the rest of the connections, which are dynamical and affect the equations of the motion. We concentrate in scenarios that depart from the $Q=$const. case, which just reproduces General Relativity with a cosmological constant, and derive novel vacuum solutions for a power-law $f(Q)$ function.

19 pages, 5 figures, Latex2e source file, updated version, to appear in PRD

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Cited by in corpus (40)

• Cosmology in $f(Q)$ gravity: A unified dynamical system analysis at background and perturbation levels
• Non-metricity with bounday terms: $f(Q,C)$ gravity and cosmology
• Late-time cosmology with phantom dark-energy in $f(Q)$ gravity
• On the viability of $f(Q)$ gravity models
• Phantom cosmological model with observational constraints in $f(Q)$ gravity
• Coincident gauge for static spherical field configurations in symmetric teleparallel gravity
• Data reconstruction of the dynamical connection function in $f(Q)$ cosmology
• Phase-space analysis of a novel cosmological model in $f(Q)$ theory
• Modelling the Accelerating Universe with $f(Q)$ Gravity: Observational Consistency
• Energy condition bounds on $f(Q)$ model parameters in a curved FLRW universe
• How different connections in flat FLRW geometry impact energy conditions in $f(Q)$ theory?
• Constraints on $f(Q)$ logarithmic model using gravitational wave standard sirens
• Exploring the stability of $f(Q)$ cosmology near general relativity limit with different connections
• Neutron Star in Covariant $f(Q)$ gravity
• Geometry and covariance of symmetric teleparallel theories of gravity
• Cosmological reconstruction and $\Lambda$CDM universe in $f(Q,C)$ gravity
• Spatial curvature in coincident gauge $f(Q)$ cosmology
• Stability of symmetric teleparallel scalar-tensor cosmologies with alternative connections
• Gravitational tensor and scalar modes in $f(Q,B)$ non-metric gravity
• Geometrical Trinity of Unimodular Gravity
• Polarized gravitational waves in the parity violating scalar-nonmetricity theory
• Dynamical reconstruction of the $\Lambda$CDM model in the scalar-tensor representation of $f\left(Q,T\right)$ gravity
• Maxwell-$f(Q)$ theory
• Gravitational metamaterials from optical properties of spacetime media
• Spatially covariant gravity with nonmetricity
• Perturbation Spectra of Warm Inflation in $f(Q,T)$ Gravity
• Late-time dynamics of dark energy EoS in symmetric teleparallel gravity
• Reconstructing modified and alternative theories of gravity
• Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity
• Conventionalism, cosmology and teleparallel gravity
• Probing symmetric teleparallel gravity in the early universe
• Vulnerability of f(Q) gravity theory and a possible resolution
• Phase space structure of symmetric teleparallel theory of gravity
• A note on the junction conditions in f(Q)-gravity
• Static, Cylindrically Symmetric Spacetimes in the Coincident f(Q) Gravity
• Implications of $f(R)$ gravity on late-time cosmic structure growth through a complete description of density perturbations
• Degrees of freedom of a quadratic scalar-nonmetricity theory
• Neutron stars in $f(\mathbb{Q})$ gravity
• Inflation and primordial fluctuations in $f(Q,T)$ gravity
• Static plane symmetric solutions in $f(Q)$ gravity