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