On LongWavelength of Modifications of Gravity and LateTime Acceleration

1
Fading Gravity and Self-Inflation
Justin Khoury (Perimeter Institute)
hep-th/0610???
2
Motivation Widely studied modifications of
gravity, e.g. large extra dimensions, typically
lead to stronger gravity at short distances.
2 ways to see this
1. Deviation from inverse-square law
2. Modified Friedmann eqn in brane-world models

• Need faster expansion at fixed density in order
  for universe to expand forever (since k0).

3
BUT What if gravity gets weaker (and shuts off)
at short distances?

• Can you still have inflation?

• Do you need inflation?

• Does it offer alternatives to the inflationary
  paradigm?

4
Our idea Shut off the graviton propagator at
large momentum
Non-perturbative effects in string theory
(Tseytlin 95) Tachyon action in open string
field theory p-adic string theory (Brekke,
Freund, Olson, Witten 88) Fat Graviton scenario
(Sundrum 97)
where
Form factor must be analytic, so no new degrees
of freedom
e.g.,

• Find novel inflationary solutions without
  scalar field or other stress energy

• Not equivalent to a scalar-tensor theory

• Genuinely different than scalar-driven inflation

5
Modified (horrific) Einsteins equations
necessary to maintain Bianchi identity
Effective Newtons constant
2 key observations
1. Pure de Sitter doesnt care
(since )
Thus pure dS is oblivious to form factor
6
2. But small deviations from dS care a lot
of order dH/dt
for HL gt 1
Modified cosmological eqn roughly of the form
i.e.,

• Inflating solution if HL gt 1

7
More explicit sketch

• Relativistic and covariant action is

Note as F?1 theory reduces to GR

• Quick check in weak-field limit, have etc.

which is action for massless spin-2 with modified
propagator
8
A fun weekend in Waterloo.
where
with
9
Another fun weekend in Waterloo

• Substitute FRW ansatz keeping terms at most of
  order dH/dt
• (i.e. ignoring d2H/dt2, (dH/dt)2, ).

• Equations simplify tremendously and find

10
Exiting self-inflating phase

• Since dH/dt lt 0, eventually reach F?1 and
  inflation ends.

• Moreover, recall that as F?1 theory reduces to GR

• Meanwhile, when dH/dt H2 particle
• production is efficient. This is the
  dominant
• reheating mechanism here.

Ford (87) Grishchuk Sidorov (90) Spokoiny
(93)
Conjecture graceful exit into normal
radiation-dominated phase at TL-1
11
Perturbations Can study evolution of
fluctuations about self-inflating solution.

• Density (scalar) perturbations are nearly
  scale-inv, with amplitude

where
and spectral tilt

• BUT tensor spectrum is very blue

Amplitude of gravity waves too small to be
observed, like ekpyrotic.
12
Robustness of effective action

• Slow-evolution approximation gets better as HL????

• Generic corrections to effective action are less
  and less relevant
• as HL????

e.g.
negligible compared to from form factor
e.g.
Effectively renormalizes form factor
13
Summary and future avenues

• Presented a theory where gravity shuts off at
  short distances

• To my knowledge, theory cant be rewritten as
  some scalar-tensor
• theory

• Find novel inflationary solutions to the vacuum
  eqns.

• Density perturbations basically degenerate with
  scalar-driven inf.

• BUT gravity waves have blue tilt
  distinguishing feature from scalar infn.