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Ishwaree Neupane University of Canterbury New Zealand. Dark Energy Constraints on Modified Gravities. Spring Symposium 2008 A Decade of Dark Energy May 5, 2008, STScI , Baltimore.

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ishwaree neupane university of canterbury new zealand
Ishwaree Neupane

University of Canterbury

New Zealand

Dark Energy Constraints on Modified Gravities

Spring Symposium 2008

A Decade of Dark Energy

May 5, 2008, STScI, Baltimore


There has been a renewal of interest in scenarios that propose alternatives to the standard model of dark energy – i.e. the cosmological constant

The proposals are of differing origin as well as motivations: some are based on higher dimensional braneworld models, others on scalar-tensor theories.


A simple theory of cosmic acceleration

(or quintessence), with a canonically normalized scalar field, is described by the Lagrangian

Observations require so unlike a naïve expectation the leading corrections to cosmological parameters arise from terms that are quadratic in the curvature.


James T. Wheeler: A Strong Advocate of Modified Gravity

The most general gravitational Lagrangian which can be constructed from the curvature two-form, the vielbein one-form, and tensors invariant in the tangent space involves

dimensionally extended Euler characteristics densities

Cosmology requires FRW and non-constant scalar couplings, i.e.

So, the Gauss-Bonnet density would affect the field equations

(even in four dimensions) because its coefficient is not constant

The coupling can be eliminated by a redefinition of the metric

gauss bonnet dark energy
Gauss-Bonnet Dark Energy

An exact non-singular inflationary solution

The coupling may grow with time but not the term

an inflationary solution
An Inflationary Solution

Choose the gauge

We can think of as well as

as both being of order at horizon exit


IPN: hep-th/0605266


The Simplest Potentials

hold some validity as a post-inflation approximation

Koivisto & Mota


Solid lines (SNe IA plus CMBR shift parameter)

Shaded regions (including Baryon Acoustic Oscillation scale)

ghost and superluminal modes
Ghost and Superluminal modes

Tensor modes

Scalar modes


Observing the effects of a scalar-GB coupling?

The growth of matter fluctuations

is the matter density contrast

In conventional models


if dark energy is the cosmological constant

For an extra dimensional

modification of gravity: DGP


L. Guzzo et al. arXiv:0802.1944 

growth of matter perturbations
Growth of matter perturbations

With the input the observational limit on growth factor

implies that

on cosmological scales




The choice


To get

we simply require

IPN & C. Scherer: arXiv:0712.2468 [JCAP:0805]


Coupled Dark Energy (Quintessence)

Local GR constraints on and its derivatives

(Damour et al. 1993, Esposito-Farese 2003)







A time-varying matter-quintessence coupling affects both the dark energy EoS and the Hubble parameter

in an interesting way:

For the exponential coupling

The Hubble parameter in the physical Jordan frame is

A positive may increase the chi-squared minimized value of




Top to bottom

is minimized for

Where is the usual

post-Newtonian parameter

we get

For the best fit value

  • 1) Scalar-Gauss-Bonnet gravity is a healthy modification of Einstein’s GR, irrespective of a type of background chosen. The theory is promising as it
  • naturally connects the classical GR with superstring theory through its low energy description.
  • admits non-singular cosmological solutions, both inflationary and non-inflationary types.
  • 2) But it is not by default that any such effective theory becomes free from ghosts or short distance instabilities. This well depends on the type of the scalar-curvature couplings that one would allow.
  • 3) The case of decreasing due to the parameter of the non-minimal coupling corresponds to a time-varying Newton’s constant that usually boosts acceleration and decreases the dark EoS