HAUNTINGS HAUNTINGS Nemanja Kaloper Nemanja Kaloper UC Davis UC Davis Based on: work with C. Charmousis, R. Gregory, A. Padilla; and work in preparation with D. Kiley. Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Overview Overview � Who cares? Who cares? � � Chasing ghosts in DGP Chasing ghosts in DGP � � Codimension Codimension- -1 case 1 case � � Specteral Specteral analysis: diagnostics analysis: diagnostics � � Shock therapy Shock therapy � � Shocking codimension Shocking codimension- -2 2 � � Gravity of photons = electrostatics on cones Gravity of photons = electrostatics on cones � � Gravitational See Gravitational See- -Saw Saw � � Summary Summary � Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
The Concert of Cosmos? The Concert of Cosmos? � Einstein’s GR: a beautiful theoretical framework for Einstein’s GR: a beautiful theoretical framework for � gravity and cosmology, consistent with numerous gravity and cosmology, consistent with numerous experiments and observations: experiments and observations: � Solar system tests of GR Solar system tests of GR New tests? New tests? � � Sub Sub- -millimeter (non)deviations from Newton’s law millimeter (non)deviations from Newton’s law New tests? New tests? � � Concordance Cosmology! Concordance Cosmology! Or, Dark Discords? Or, Dark Discords? � � How well do we How well do we REALLY REALLY know gravity? know gravity? � � Hands Hands- -on observational tests confirm GR at scales between on observational tests confirm GR at scales between � roughly 0.1 mm 0.1 mm and and - - say say - - about about 100 are we certain roughly ; are we 100 MPc MPc; certain that GR remains valid at shorter shorter and and longer longer distances? distances? that GR remains valid at Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Headaches Headaches � Changing gravity → adding new Changing gravity → adding new DOFs DOFs in the IR in the IR � � They can be problematic: They can be problematic: � � Too light and too strongly coupled → new long range forces Too light and too strongly coupled → new long range forces � Observations place bounds on these! Observations place bounds on these! � Negative mass squared Negative mass squared or negative residue of the pole in the or negative residue of the pole in the � propagator for the new DOFs DOFs: : tachyons tachyons and/or and/or ghosts propagator for the new ghosts I nstabilities can render the theory nonsensical! I nstabilities can render the theory nonsensical! Caveat emptor: this need not be a theory killer; it means that a Caveat emptor: this need not be a theory killer; it means that a naive perturbative perturbative description about some background is very description about some background is very naive bad. Hence one *must* *must* develop a meaningful develop a meaningful perturbative perturbative regime regime bad. Hence one before surveying phenomenological issues and applications. before surveying phenomenological issues and applications. Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
DGP Braneworlds Braneworlds DGP � Brane Brane- -induced gravity induced gravity ( : , 2000) : � (Dvali Dvali, , Gabadadze Gabadadze, , Porrati Porrati, 2000) � Ricci terms BOTH in the bulk and on the end Ricci terms BOTH in the bulk and on the end- -of of- -the the- - � world brane brane, arising from e.g. wave function , arising from e.g. wave function world renormalization of the graviton by brane brane loops loops renormalization of the graviton by � May appear in string theory May appear in string theory ( (Kiritsis Kiritsis, , Tetradis Tetradis, , Tomaras Tomaras, 2001; , 2001; � Corley, Lowe, Ramgoolam Corley, Lowe, Ramgoolam, 2001) , 2001) � Related works on exploration of Related works on exploration of brane brane- -localized localized � radiative corrections corrections (Collins, radiative (Collins, Holdom Holdom, 2000) , 2000) Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Codimension- -1 1 Codimension � Action: for the case of codimension Action: for the case of codimension- -1 1 brane brane, , � � Assume ∞ bulk: 4D gravity has to be mimicked by the Assume ∞ bulk: 4D gravity has to be mimicked by the � exchange of bulk DOFs DOFs! ! exchange of bulk th dimension is concealed by the � 5 5 th dimension is concealed by the brane brane curvature curvature � 2 for enforcing momentum transfer → → 1/p 1/p 2 for p > 1/r p > 1/r c enforcing momentum transfer (DGP, c (DGP, 2000; Dvali Dvali, , Gabadadze Gabadadze, 2000): , 2000): 2000; Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Strong coupling caveats Strong coupling caveats In massive gravity, naïve linear perturbation theory in massive In massive gravity, naïve linear perturbation theory in massive � � gravity on a flat space breaks down → → idea: nonlinearities improve idea: nonlinearities improve gravity on a flat space breaks down the theory and yield continuous limit ( the theory and yield continuous limit , 1972) ? ? (Vainshtein Vainshtein, 1972) There are examples without There are examples without IvDVZ IvDVZ discontinuity in curved discontinuity in curved � � backgrounds ( rock of salt!) backgrounds with a rock . (dS dS with a of salt!) ; 2000) . ( (Kogan Kogan et al et al ; ; Karch Karch et al et al ; ; Porrati Porrati; 2000) Key: the scalar graviton is strongly coupled at a scale much big Key: the scalar graviton is strongly coupled at a scale much bigger ger � � than the gravitational radius (a long list of people… sorry, y’all!) than the gravitational radius . (a long list of people… sorry, y’all!) . In DGP a naïve expansion around flat space also breaks down at In DGP a naïve expansion around flat space also breaks down at � � macroscopic scales ( macroscopic scales (Deffayet Deffayet, , Dvali Dvali, , Gabadadze Gabadadze, , Vainshtein Vainshtein, 2001; , 2001; Luty Luty, , Porrati Porrati, , , 2003). Including curvature may push it down to Including curvature may push it down to Rattazi, 2003; , 2003; Rubakov Rubakov, 2003). Rattazi about ~ ~ 1 cm 1 cm ( ( Rattazi about ). , 2004 ). Rattazi & & Nicolis Nicolis, 2004 LPR also claim a ghost in the scalar sector on the self- -accelerating accelerating LPR also claim a ghost in the scalar sector on the self � � branch; after some vacillation, others seem to agree branch; after some vacillation, others seem to agree ( ( Koyama Koyama 2 2 ; Koyama, ; Koyama, , 2005 ). ). 2005; 2005; Gorbunov Gorbunov, Koyama, , Koyama, Sibiryakov Sibiryakov, 2005 Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Perturbing cosmological vacua vacua Perturbing cosmological Difficulty: equations are hard, perturbative perturbative treatments of treatments of both Difficulty: equations are hard, both � � background and interactions subtle... Can we be more precise? background and interactions subtle... Can we be more precise? An attempt: construct realistic backgrounds; solve An attempt: construct realistic backgrounds; solve � � Look at the vacua vacua first: first: Look at the � � : , 1998) : Symmetries require (see e.g. N.K, A. Symmetries require (see e.g. N.K, A. Linde Linde, 1998) � � where 4d metric is de Sitter. where 4d metric is de Sitter. Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Codimension- -1 1 vacua vacua Codimension Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Normal and self- -inflating branches inflating branches Normal and self The intrinsic curvature and the tension related by ( ( N.K.; Deffayet,2000 ) N.K.; Deffayet,2000 ) The intrinsic curvature and the tension related by � � ε = = ± 1 an integration constant; an integration constant; ε ε = = - -1 1 normal branch, normal branch, ε ± 1 � � i.e. this reduces to the usual inflating brane brane in 5D! in 5D! i.e. this reduces to the usual inflating ε = =1 1 self self- -inflating branch, inflates even if tension vanishes! inflating branch, inflates even if tension vanishes! ε � � Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Specteroscopy Specteroscopy Logic: start with the cosmological vacua vacua and perturb the bulk & and perturb the bulk & Logic: start with the cosmological � � brane system, allowing for system, allowing for brane brane matter as well; gravity sector is matter as well; gravity sector is brane But, there are still unbroken gauge invariances invariances of the of the bulk+brane bulk+brane But, there are still unbroken gauge � � system! Not all modes are physical. system! Not all modes are physical. The analysis here is linear linear - - think of it as a diagnostic tool. But: it think of it as a diagnostic tool. But: it The analysis here is � � reflects problems with perturbations at lengths > Vainshtein Vainshtein scale. scale. reflects problems with perturbations at lengths > Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
Gauge symmetry I Gauge symmetry I Infinitesimal transformations Infinitesimal transformations � � The perturbations change as The perturbations change as � � Set e.g. and to zero; that leaves us with and Set e.g. and to zero; that leaves us with and � � Nemanja Kaloper, UC Davis Nemanja Kaloper, UC Davis
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