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�

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�

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�

•  Actually two cutoffs:�

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�

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

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�

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

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�

•  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: �

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�

•  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

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�

•  Why consider quantum issues in classical regimes?�

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�

•  Why consider quantum issues in classical regimes?�

•  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: �

Background Dependence & Domain of Validity�

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

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

Background Dependence & Domain of Validity�

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

•  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�

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: �

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

Background Dependent: Expand in deviations from our cosmological background�

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�

•  Scaling rule: �

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

•  Consistent only for�

Standard Version � PNGB Version �

•  Scaling rule: �

•  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�

Background Independent, Covariant Approach (cont)�

•  Final result �

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

Background Independent, Covariant Approach (cont)�

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.�