1. Fading Gravity and Self-Inflation Justin Khoury 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. 1. Deviation from inverse-square law: 2 ways to see this: 2. Modified Friedmann eqn in brane-world models:  Need faster expansion at fixed density in order for universe to expand forever (since k=0).

3. Can you still have inflation? Can you still have inflation? Do you need inflation? Do you need inflation? Does it offer alternatives to the inflationary paradigm? Does it offer alternatives to the inflationary paradigm? BUT: What if gravity gets weaker (and shuts off) at short distances?

4.  Genuinely different than scalar-driven inflation Our idea: Shut off the graviton propagator at large momentum Find novel inflationary solutions without scalar field or other stress energy Find novel inflationary solutions without scalar field or other stress energy Not equivalent to a scalar-tensor theory Not equivalent to a scalar-tensor theory where 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) Form factor must be analytic, so no new degrees of freedom e.g.,

5. Modified (horrific) Einstein’s equations: 1. Pure de Sitter doesn’t care 2 key observations: necessary to maintain Bianchi identity Effective Newton’s constant (since ) Thus pure dS is oblivious to form factor

6. 2. But small deviations from dS care a lot: of order dH/dt Modified cosmological eqn roughly of the form: i.e.,  Inflating solution if HL > 1 for HL > 1

7. More explicit sketch: Relativistic and covariant action is: Quick check: in weak-field limit, have etc. which is action for massless spin-2 with modified propagator Note: as F  theory reduces to GR

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 d 2 H/dt 2, (dH/dt) 2, …). Substitute FRW ansatz keeping terms at most of order dH/dt (i.e. ignoring d 2 H/dt 2, (dH/dt) 2, …). Equations simplify tremendously and find:

10. Exiting self-inflating phase: Since dH/dt < 0, eventually reach F  and inflation ends. Meanwhile, when dH/dt ~ H 2 particle production is efficient. This is the dominant reheating mechanism here. Meanwhile, when dH/dt ~ H 2 particle production is efficient. This is the dominant reheating mechanism here. Moreover, recall that as F  theory reduces to GR Ford (‘87) Grishchuk & Sidorov (‘90) Spokoiny (‘93) Conjecture: graceful exit into normal radiation-dominated phase at T~L -1

11. Perturbations: Can study evolution of fluctuations about self- inflating solution. Density (scalar) perturbations are nearly scale-inv, with amplitude and spectral tilt where 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  Generic corrections to effective action are less and less relevant as HL  e.g. negligible compared tofrom 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 can’t be rewritten as some scalar-tensor theory To my knowledge, theory can’t 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.