Dark energy and gravity

Abstract

I review the problem of dark energy focussing on cosmological constant as the candidate and discuss what it tells us regarding the nature of gravity. Section 1 briefly overviews the currently popular "concordance cosmology" and summarizes the evidence for dark energy. It also provides the observational and theoretical arguments in favour of the cosmological constant as a candidate and emphasizes why no other approach really solves the conceptual problems usually attributed to cosmological constant. Section 2 describes some of the approaches to understand the nature of the cosmological constant and attempts to extract certain key ingredients which must be present in any viable solution. In the conventional approach, the equations of motion for matter fields are invariant under the shift of the matter Lagrangian by a constant while gravity breaks this symmetry. I argue that until the gravity is made to respect this symmetry, one cannot obtain a satisfactory solution to the cosmological constant problem. Hence cosmological constant problem essentially has to do with our understanding of the nature of gravity. Section 3 discusses such an alternative perspective on gravity in which the gravitational interaction-described in terms of a metric on a smooth spacetime-is an emergent, long wavelength phenomenon, and can be described in terms of an effective theory using an action associated with normalized vectors in the spacetime. This action is explicitly invariant under the shift of the matter energy momentum tensor T ab → T ab + g ab and any bulk cosmological constant can be gauged away. Extremizing this action leads to an equation determining the background geometry which gives Einstein's theory at the lowest order with Lanczos-Lovelock type corrections. In this approach, the observed value of the cosmological constant has to arise from the energy fluctuations of degrees of freedom located in the boundary of a spacetime region.

Surface density of spacetime degrees of freedom from equipartition law in theories of gravity

“…For a macroscopic system like a gas, one can obtain the dynamical equations from maximizing an entropy functional S[q A ] expressed in terms of appropriate variables q A . Analogously, one should be able to derive the field equations of gravity from maximizing a suitable entropy functional of spacetime [10]. However, as we said before, there is one crucial difference between thermodynamics 4 Note that in Einstein's theory, we get ∆n = ∆A/L 2 P .…”

“…3, I will reverse the logic and indicate how the field equations of any diffeomorphism invariant theory of gravity can be obtained from an entropy extremising principle. This has already been done in earlier papers [10] and hence my discussion will be limited to stressing some new features and making the logical connections. Sec.4 comments on the possible manner in which the key results of the earlier sections can arise in a microscopic theory of gravity and the last section gives brief conclusions.…”

“…So we need to generalize this notion and introduce a suitable vector field in its place. This issue is conceptually more involved but -fortunately -has already been addressed [10,14]. We know from the study of accelerated observers in flat spacetime that the null surfaces X = ±T in the inertial coordinates (T, X) appear as the local horizon to the observer moving on the uniformly accelerated trajectory X 2 − T 2 = κ −2 and has to be endowed with temperature and entropy.…”

“…It can be shown [1,10] that maximizing (S grav + S matter ) for all null vectors k a simultaneously 5 leads to the field equations in Eq. (8).…”

Emergent perspective of gravity and dark energy

“…We obtain (on using the generalized Bianchi identity and the condition ∇ a T a b = 0) the result [41,42]:…”