Alternative and modified gravity theories

The paper proposes gravity leaking into extra dimensions as an alternative explanation for cosmic acceleration instead of invoking dark energy or a cosmological constant.

“We discuss the idea that the accelerated Universe could be the result of the gravitational leakage into extra dimensions on Hubble distances rather than the consequence of non-zero cosmological constant.”◌ not checked against the paper’s text as it now stands

The paper explicitly introduces a dark energy component with equation of state parameter w_X into the conventional Friedmann equation for comparison with its model.

“Here, in addition to the matter and curvature contributions we have included the density of a dark energy component Ω_X with equation of state parameter w_X. When w_X=-1, the dark energy acts in the same way as a cosmological constant, and the corresponding Ω_X will be denoted as Ω_Λ in the following.”◌ not checked against the paper’s text as it now stands

The paper shows that its extra-dimensional model mimics the effect of a dark energy component with equation of state w_X greater than -1, rather than an exact cosmological constant.

“our model mimics the cosmological constant in producing the late-time accelerated expansion. However, as is also apparent from this plot, for the same flat spatial geometry and the same amount of non-relativistic matter, our model does not produce exactly the same acceleration as a standard cosmological constant, but it rather mimics the one obtained from a dark energy component with w_X > -1.”◌ not checked against the paper’s text as it now stands

The paper quantitatively compares its model against various dark energy models with different constant w_X values using luminosity distance and the Alcock-Paczynski test to assess distinguishability.

“Plot of d_L(z)/d_L^ref(z) for various models of dark energy with constant equation of state parameters w_X in standard cosmology (solid lines) as compared with the outcome of the model consider in this paper (dashed and dotted lines).”◌ not checked against the paper’s text as it now stands

The paper introduces a braneworld dark energy model where a scalar curvature term on the brane, generated by one-loop quantum corrections, drives late-time cosmic acceleration without requiring exotic matter fields.

“We explore a new class of braneworld models in which the scalar curvature of the (induced) brane metric contributes to the brane action. The scalar curvature term arises generically on account of one-loop effects induced by matter fields residing on the brane. Spatially flat braneworld models can enter into a regime of accelerated expansion at late times.”◌ not checked against the paper’s text as it now stands

The paper shows that this braneworld dark energy can effectively have an equation of state w < -1 without suffering the pathologies of conventional phantom energy models.

“Braneworld models, on the other hand, have the capacity to endow dark energy with exciting new possibilities (including w < -1) without suffering from the problems faced by phantom energy.”◌ not checked against the paper’s text as it now stands

The paper demonstrates that for a subclass of parameters, the braneworld dark energy and cosmic acceleration are transient, with the universe reverting to matter domination at late times, potentially reconciling acceleration with string/M-theory constraints.

“For a subclass of parameter values, braneworld dark energy and the acceleration of the universe are transient phenomena. In these models, the universe, after the current period of acceleration, re-enters the matter-dominated regime so that the deceleration parameter q(t) → 0.5 when t ≫ t_0, where t_0 is the present epoch. Such models could help reconcile an accelerating universe with the requirements of string/M-theory.”

The paper proposes deriving dark energy behavior geometrically from curvature invariants of fourth-order gravity rather than from a matter-energy scalar field.

“In this paper, we want to investigate if the quintessential scheme can be achieved in a geometrical way by taking into account higher order theories of gravity.”◌ not checked against the paper’s text as it now stands

It defines effective curvature pressure and curvature density terms that act as an alternative source of dark energy (cosmic acceleration) in place of standard quintessence.

“From the curvature-stress-energy tensor, we can define a curvature pressure p_(curv)=1/f'(R){2(ȧ/a)Ṙf”(R)+R̈f”(R)+Ṙ^2f”'(R) -1/2[f(R)-Rf'(R)] }, and a curvature density ρ_(curv)=1/f'(R){1/2[f(R)-Rf'(R)] -3(ȧ/a)Ṙf”(R) }.”◌ not checked against the paper’s text as it now stands

The paper derives explicit accelerated power-law cosmological solutions from f(R)=f0 R^n models that reproduce a deceleration parameter matching current dark-energy-driven acceleration observations.

“we obtain the exact solutions β=2; n=-1,3/2; k=0. In both cases, the deceleration parameter is q_0=-1/2, in perfect agreement with the observational results.”◌ not checked against the paper’s text as it now stands

The paper proposes that cosmic acceleration can be explained by modifying the gravitational action rather than invoking dark energy.

“We show that cosmic acceleration can arise due to very tiny corrections to the usual gravitational action of general relativity of the form R^n, with n<0. This eliminates the need for dark energy, though it does not address the cosmological constant problem.”◌ not checked against the paper’s text as it now stands

The authors note that dark energy is conventionally introduced within general relativity as a fluid with negative pressure, but this approach has serious theoretical problems.

“Cosmic speed-up can be accommodated within general relativity by invoking a mysterious cosmic fluid with large negative pressure, dubbed dark energy. The simplest possibility for dark energy is a cosmological constant; unfortunately, the smallest estimates for its value are 55 orders of magnitude too large (for reviews see […]).”◌ not checked against the paper’s text as it now stands

They show their gravitational model can mimic dark energy with an equation-of-state parameter of w=-2/3 through power-law acceleration.

“Thus, the Universe evolves to late-time power-law inflation, with observational consequences similar to dark energy with equation-of-state parameter w_ DE=-2/3.”

The paper frames the dark energy problem as the problem of Ω being less than 1, requiring either new matter/energy or modified gravity to reach the critical density.

“The problem of dark energy is the problem of Ω: Ω=8π Gρ_M/3H^2 <1. Since Ω can be regarded as the ratio of the right-hand-side of the Einstein equation (matter) to the left-hand-side of the Einstein equation (curvature=gravity), in order to make Ω=1 one requires either (i) introduction of new form of matter(energy): dark energy or (ii) modification of gravity in the large, so that the total energy density is equal to the critical density, which is required by theory (inflation) or by observation (WMAP).”◌ not checked against the paper’s text as it now stands

The paper analyzes the CDTT R^-1 gravity model, which was proposed as an alternative to dark energy, and shows via its scalar-tensor equivalent that it is excluded by solar system experiments due to a very light scalar field with ω=0.

“The second example is CDTT model […]: F(R)=R-μ^4/R with μ∼ H_0≃ 10^-42GeV. Again, in terms of φ, the effective potential is given by V(φ)=μ^2e^-2√(2/3)κφκ^2√(e^√(2/3)κφ-1). Evaluating V” around ϕ=R∼ H_0^2 (κφ∼ 1) gives the effective mass squared of order μ^2 (and tachyonic for 8/9<e^√(2/3)κφ<2), which is very light. Together with ω=0, the solar system experiments exclude such a theory.”◌ not checked against the paper’s text as it now stands

The paper concludes that such R^-1-type modified gravity theories (dubbed 'c-essence') proposed as alternatives to dark energy are ruled out by observational constraints, leaving open whether other gravity modifications could work.

The paper proposes modified gravity with negative powers of curvature as a gravitational alternative to dark energy, eliminating the need for dark energy.

“The modified gravity, which eliminates the need for dark energy and which seems to be stable, is considered.”◌ not checked against the paper’s text as it now stands

It shows that the terms with negative powers of curvature act as effective dark energy driving current cosmic acceleration.

“The terms with positive powers of the curvature support the inflationary epoch while the terms with negative powers of the curvature serve as effective dark energy, supporting current cosmic acceleration.”◌ not checked against the paper’s text as it now stands

The work argues that a gravitational foundation for cosmic acceleration is more natural than introducing dark energy as a mysterious cosmic fluid with negative pressure.

“Clearly, having the gravitational foundation for description of current cosmic acceleration seems to be much more natural than the introduction by hands of the mysterious dark energy, cosmic fluid with negative pressure.”◌ not checked against the paper’s text as it now stands

The paper proposes a new dark energy model based on scalar-Gauss-Bonnet coupling inspired by string/M-theory to explain the current cosmic acceleration.

“We propose the Gauss-Bonnet dark energy model inspired by string/M-theory where standard gravity with scalar contains additional scalar-dependent coupling with Gauss-Bonnet invariant.”◌ not checked against the paper’s text as it now stands

It demonstrates that this model can produce an effective phantom or quintessence dark energy phase depending on whether the scalar is phantom or canonical with nonzero potential.

“It is demonstrated that effective phantom (or quintessence) phase of late universe may occur in the presence of such term when the scalar is phantom or for non-zero potential (for canonical scalar).”◌ not checked against the paper’s text as it now stands

The paper shows that the dark energy equation of state can cross or vary around w=-1 as curvature increases, since the GB term becomes dominant at high curvature.

“However, with the increase of the curvature the GB term may become dominant so that phantom phase is transient and w=-1 barrier may be passed.”◌ not checked against the paper’s text as it now stands

The paper proposes modified Gauss-Bonnet gravity, adding an arbitrary function f(G) to the Einstein action, as a gravitational alternative to dark energy.

“We suggest the modified gravity where some arbitrary function of Gauss-Bonnet (GB) term is added to Einstein action as gravitational dark energy.”◌ not checked against the paper’s text as it now stands

The paper shows that this modified GB gravity can describe late-time cosmic acceleration with various effective equations of state (cosmological constant, quintessence, or phantom).

“It is demonstrated that modified GB gravity may describe the most interesting features of late-time cosmology: the transition from deceleration to acceleration, crossing the phantom divide, current acceleration with effective (cosmological constant, quintessence or phantom) equation of state of the universe.”◌ not checked against the paper’s text as it now stands

The paper demonstrates that this GB-based dark energy alternative can pass solar system tests, unlike some other modified gravity proposals.

“It is shown that such theory may pass solar system tests.”◌ not checked against the paper’s text as it now stands

The paper reviews modified gravity theories as a gravitational alternative to dark energy models based on scalar fields or fluids.

“We review various modified gravities considered as gravitational alternative for dark energy.”◌ not checked against the paper’s text as it now stands

It shows that such modified gravity models can naturally describe effective cosmological constant, quintessence, or phantom dark energy eras and the transition from deceleration to acceleration.

“they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease.”◌ not checked against the paper’s text as it now stands

The paper proposes that the coincidence problem of dark energy can be explained as a manifestation of the universe's expansion within modified gravity models.

“The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned.”◌ not checked against the paper’s text as it now stands

The paper proposes reinterpreting dark energy (and dark matter) as manifestations of shortcomings in standard General Relativity rather than as unknown exotic components.

“The problem could be completely reversed considering dark matter and dark energy as "shortcomings" of General Relativity in its simplest formulation (a linear theory in the Ricci scalar R, minimally coupled to the standard perfect fluid matter) and claiming for the "correct" theory of gravity as that derived by matching the largest number of observational data, without imposing any theory a priori.”◌ not checked against the paper’s text as it now stands

The paper reviews and critiques the standard cosmological constant and quintessence explanations of dark energy, highlighting their fine-tuning and coincidence problems.

“Although it is the best fit to most of the available astrophysical data […], the ΛCDM model fails in explaining why the inferred value of Λ is so tiny (120 orders of magnitude lower!) if compared with the typical vacuum energy values predicted by particle physics and why its energy density is today comparable to the matter density (the so called coincidence problem).”◌ not checked against the paper’s text as it now stands

The paper surveys extended/modified theories of gravity (f(R) gravity) as an alternative framework to explain the accelerated expansion attributed to dark energy without invoking exotic fluids.

The paper proposes a class of f(R) gravity models in which the cosmological constant is zero in flat space-time but appears effectively in curved space-time, distinguishing this dark energy behavior from the standard LambdaCDM.

“a class of models is proposed which produce viable cosmology different from the LambdaCDM one at recent times and satisfy cosmological, Solar system and laboratory tests. These models have both flat and de Sitter space-times as particular solutions in the absence of matter. Thus, a cosmological constant is zero in flat space-time, but appears effectively in a curved one for sufficiently large R.”◌ not checked against the paper’s text as it now stands

It identifies a potential observational signature ('smoking gun') for these f(R) dark energy models via a discrepancy in the slope of the primordial power spectrum from galaxy surveys versus CMB.

“A 'smoking gun' for these models would be small discrepancy in values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations.”◌ not checked against the paper’s text as it now stands

The paper points out a new problem for f(R)-based dark energy models regarding possible overproduction of massive scalar particles (scalarons) in the early Universe.

“a new problem for dark energy models based on f(R) gravity is pointed which is connected with possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.”

The paper reviews how f(R) gravity models can serve as modified-gravity alternatives to explain the late-time cosmic acceleration attributed to dark energy.

“Dark energy models based on f(R) theories have been extensively studied as the simplest modified gravity scenario to realize the late-time acceleration.”◌ not checked against the paper’s text as it now stands

It discusses a specific f(R) dark energy model, f(R)=R-α/R^n, and shows that it suffers from matter instabilities, fails local gravity constraints, and lacks a standard matter-dominated epoch.

“The model with a Lagrangian density f(R)= R-α /R^n (α>0, n>0) was proposed for dark energy in the metric formalism […]. However it was shown that this model is plagued by a matter instability […] as well as by a difficulty to satisfy local gravity constraints […]. Moreover it does not possess a standard matter-dominated epoch because of a large coupling between dark energy and dark matter […].”◌ not checked against the paper’s text as it now stands

The paper reviews the derivation of conditions for cosmologically viable f(R) dark energy models and the construction of models satisfying both cosmological and local gravity constraints.

“Amendola et al. […] derived conditions for the cosmological viability of f(R) dark energy models. In local regions whose densities are much larger than the homogeneous cosmological density, the models need to be close to GR for consistency with local gravity constraints. A number of viable f(R) models that can satisfy both cosmological and local gravity constraints have been proposed in […].”

The review discusses the discovery that dark energy is required to explain the observed accelerating expansion of the Universe, treating it as part of the evidence motivating modified gravity.

“More recently, `dark energy' has also been found to be required in order to explain the apparent accelerating expansion of the Universe.”◌ not checked against the paper’s text as it now stands

The paper surveys the current observational evidence for the 'dark universe' (including dark energy) and explains why it has become the standard cosmological paradigm.

“In this section we also survey the current evidence for the `dark universe', and explain why it has become the standard paradigm.”◌ not checked against the paper’s text as it now stands

The authors highlight the puzzling composition of the Universe implied by dark energy and dark matter as a motivation for considering that General Relativity might not be the correct theory on the largest scales.

“Indeed, if General Relativity is correct, it now seems that around 96% of the Universe should be in the form of energy densities that do not interact electromagnetically. Such an odd composition, favoured at such high confidence, has led some to speculate on the possibility that General Relativity may not, in fact, be the correct theory of gravity to describe the Universe on the largest scales.”