effective field theory and modiﬁed gravityflanagan/talks/oxford.pdf · effective field theory and...

Effective Field Theory and Modified Gravity�

Cosmological Tests of Gravity, University of Oxford �

14 March 2013 �

Éanna Flanagan, Cornell�

J. Bloomfield, EF, JCAP 10, 039 (2012); J. Bloomfield, EF, M. Park, S. Watson, arXiv:1211.7054�

Modified Gravity �

• Definition: �

for which predictions for gravitational observations are modified�

• Motivations: New observational windows, dark matter puzzles on galactic scales�

• Status: �

Effective Field Theories of Modified Gravity�

• Which is better? Are they complementary?�

• Type I: Covariant, independent of background cosmology � Weinberg (2008); Burgess, Lee and Trott (2009); Park, Zurek and Watson (2010); Jiminez, Talavera and Verde (2011); Bloomfield and EF (2012); Jimenez et. al. (2012); Mueller, Bean and Watson (2012). �

• Type II: Expands about given background cosmology� Cheung et. al (2008); many others; Creminelli, d’Amico, Norena and Vernizzi (2009); Battye and Pearson (2012); Gubitosi, Piazza and Vernizzi (2012); Bloomfield, EF, Park and Watson (2012). �

Applied to inflationary era �

Applied to present cosmic acceleration �

• How all-encompassing is effective field theory approach?�

Effective Field Theory Paradigm: Review �• A method of defining and parameterizing all approximate quantum field theories consistent with a given field content, set of symmetries, and energy cutoff�


• High energy physics assumed to be random, arbitrary�

• Predictive and restrictive, excludes as fine-tuned models with�


• Actually two cutoffs:�


• Actually two cutoffs:� • Framework more constraining for large cutoffs. Two cases: �


• We want to fix physical degrees of freedom: this restricts allowed operators. Gauge degrees of freedom can be added or subtracted. �


• We want to fix physical degrees of freedom: this restricts allowed operators. Gauge degrees of freedom can be added or subtracted. �

• Simplest case: 2+1 dof � • Other cases: �


• Why consider quantum issues in classical regimes?�

Inflationary modes leaving horizon

Observable modes reentering horizon

BBN

CMB

Sgr A*

Neutron stars

Solar System

Halos

Dark Energy Curvature Scale

mp H0



• Greater discriminating power than classical analysis: �‣ Exclude strong coupling (loops), eg Palatini f(R), Chameleon, Galileon �‣ Quantum instabilities (vacuum decay), eg Chern-Simons gravity�‣ Fine tuning considerations give probability measure on space of theories�

Background Dependence & Domain of Validity�

• Vacuum -> Time dependent classical solution �• Theory independent of choice of background�• Consistency: �



• Inflation, particle physics: only E relevant, simple�



• Inflation, particle physics: only E relevant, simple�

• More generally: �‣ Strong coupling energy can depend on N, eg Galileons�‣ Separate type of breakdown �

Two Classes of Effective Field Theory�Background Independent: works for all backgrounds, covariant expansion in �

Background Dependent: Expand in deviations from our cosmological background�



Covers a larger set of theories with finitely many terms: �

Background Independent, Covariant Approach�

• Scaling rule: �

• Different scaling necessary for cosmic acceleration models if all terms are O(1)�

• Consistent only for�

Background Independent, Covariant Approach�


• Different scaling necessary for cosmic acceleration models if all terms are O(1)�

• Consistent only for�

Standard Version � PNGB Version �


• Scenario (Frieman et al 1995) �

• Sum over powers of field to obtain functions of field, covariant derivative expansion �

• Yields�

Background Independent, Covariant Approach (cont)�

• Start with�

• Define effect of higher derivative terms by reducing order�

• Simplify using perturbative field redefinition freedom�


• Final result �

• Coefficients are arbitrary functions of field with specific scalings, eg �

Background Dependent Approach�

• Use 3+1 splitting: �

• Expand: �

• Specialize gauge so that �

• Most general action preserving gauge choice�

• Expand: �

Conclusions and Outlook �

• Effective field theory method useful but not a panacea�

• What do current and future data say about the coefficients?�

• The two methods that have been used in cosmology, background dependent and background independent, are complementary, but the background dependent variant is more useful.�

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