Relaxation of the Cosmological Constant

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Transkrypt:

Relaxation of the Cosmological Constant with Peter Graham and David E. Kaplan The Born Again Universe + Work in preparation + Work in progress

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Time Evolution Time evolution can change our expectations of naturalness Initial Formation + millions of years Dissipation is central - eroded sand needs to go somewhere Slow Dissipative process => light, weakly coupled field. Testable! Could Λ erode over time?

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sha1_base64="bwmnbz0eosm7trujk88czlieotk=">aaab9hicbzc7sgnbfibpxlumt6iv2awgwsrs2ihwqrvlcoycyrjnz0+siboz68xsicx5c8hgqhfbh8bot3fykttxh4gp/5zdofmhiedauo63k1tzxvvfyg8wtrz3dvek+wd1haekyy3filbnggouxglnccowmsikuscweqxujvxgejxmsbw3owt9ipyk73jgjbx8dipdvigidlnxp1hyy+5uzbm8ozqqv0dpdwbq7rs/2mhm0gilyyjq3flcxpgzvyyzgenco9wyudagpwxzldrc7wfto8fk1doh6cbkpmni1p09kdfi61eu2m6imr5ere3m/2qt1hqv/yzljduo2wxrnxxexgssaam5qmbeyajlittbcettg4gxorvscn7il5ehfl72ln/znk5hpjwcwwmcgqcxuifbqeingdzcm7zcmzn0xpx352pwmnpmm4fwr87nd1cak+4=</latexit> <latexit sha1_base64="rxkqiztuvkmhg79owu1i0qck5qy=">aaab9hicbzdlssnafizp6q3ww9wvuakwwvvj3frcfd24rgavkiyymzy0qyetodmplnc3eny4umstd+pot3f6wwjrdwmf/zmhc+ypus6udpxvq7c2vrg5vdwu7ezu7r+ud49akskkxszneci7avhimccmzppjj5vi4objoxjetuvteurfevggxyn6meklfjfktlh8bizcliekfpnjr1xxqs5m9iq4c6jur0+epf4jjv75qxsmnitramqjup7rpnrpidsmcpyuupnclnah6annujaylz/pjp7y58yj7sir5gltz9zfezmjlrrhgemmir6o5dru/k/mztq68nmm0kyjopnfucztndjtboyqsasajw0qkpm51aydyilqjqesccfd/viqtc6rruf7k8ynzfweuzidc3chbnw4gwy0gcijpmmrvfkj68v6tz7mrqvrmxmmf2r9/gcruptt</latexit> <latexit sha1_base64="rxkqiztuvkmhg79owu1i0qck5qy=">aaab9hicbzdlssnafizp6q3ww9wvuakwwvvj3frcfd24rgavkiyymzy0qyetodmplnc3eny4umstd+pot3f6wwjrdwmf/zmhc+ypus6udpxvq7c2vrg5vdwu7ezu7r+ud49akskkxszneci7avhimccmzppjj5vi4objoxjetuvteurfevggxyn6meklfjfktlh8bizcliekfpnjr1xxqs5m9iq4c6jur0+epf4jjv75qxsmnitramqjup7rpnrpidsmcpyuupnclnah6annujaylz/pjp7y58yj7sir5gltz9zfezmjlrrhgemmir6o5dru/k/mztq68nmm0kyjopnfucztndjtboyqsasajw0qkpm51aydyilqjqesccfd/viqtc6rruf7k8ynzfweuzidc3chbnw4gwy0gcijpmmrvfkj68v6tz7mrqvrmxmmf2r9/gcruptt</latexit> <latexit sha1_base64="kj9jfobhdowigzs4bbhqrpujgrg=">aaab9hicbzbns8naeiyn9avwr6phl4tf8fqsl3osevfywx5ag8pmm2mxbjzxd1moob/diwdfvppjvplv3ly5aoslcw/vzdczb5akro3rfjuljc2t7z3ybmvv/+dwqhp80tzjphi2wcis1q2orseltgw3arupqhohajvb+g5e70xqaz7irznn0y/pupkim2qs5fczgaikfgwyzwbvmlt3fylr4bvqg0lnqfwrhyysi1eajqjwpc9njz9tztgtokv0m40pzwm6xj5fswpufr44ekyurboskfh2sumw7u+jnmzat+padsbujprqbw7+v+tljrrxcy7tzkbky0vrjohjydwbenkfziipbcout7csnqi2amnzqtgqvnuvr0p7qu5zfnbrjdsijjkcwtlcggfx0ib7aeilgdzbm7zcmznxxpx352pzwnkkmvp4i+fzb0cgkmc=</latexit> <latexit sha1_base64="bwmnbz0eosm7trujk88czlieotk=">aaab9hicbzc7sgnbfibpxlumt6iv2awgwsrs2ihwqrvlcoycyrjnz0+siboz68xsicx5c8hgqhfbh8bot3fykttxh4gp/5zdofmhiedauo63k1tzxvvfyg8wtrz3dvek+wd1haekyy3filbnggouxglnccowmsikuscweqxujvxgejxmsbw3owt9ipyk73jgjbx8dipdvigidlnxp1hyy+5uzbm8ozqqv0dpdwbq7rs/2mhm0gilyyjq3flcxpgzvyyzgenco9wyudagpwxzldrc7wfto8fk1doh6cbkpmni1p09kdfi61eu2m6imr5ere3m/2qt1hqv/yzljduo2wxrnxxexgssaam5qmbeyajlittbcettg4gxorvscn7il5ehfl72ln/znk5hpjwcwwmcgqcxuifbqeingdzcm7zcmzn0xpx352pwmnpmm4fwr87nd1cak+4=</latexit> <latexit sha1_base64="rxkqiztuvkmhg79owu1i0qck5qy=">aaab9hicbzdlssnafizp6q3ww9wvuakwwvvj3frcfd24rgavkiyymzy0qyetodmplnc3eny4umstd+pot3f6wwjrdwmf/zmhc+ypus6udpxvq7c2vrg5vdwu7ezu7r+ud49akskkxszneci7avhimccmzppjj5vi4objoxjetuvteurfevggxyn6meklfjfktlh8bizcliekfpnjr1xxqs5m9iq4c6jur0+epf4jjv75qxsmnitramqjup7rpnrpidsmcpyuupnclnah6annujaylz/pjp7y58yj7sir5gltz9zfezmjlrrhgemmir6o5dru/k/mztq68nmm0kyjopnfucztndjtboyqsasajw0qkpm51aydyilqjqesccfd/viqtc6rruf7k8ynzfweuzidc3chbnw4gwy0gcijpmmrvfkj68v6tz7mrqvrmxmmf2r9/gcruptt</latexit> <latexit sha1_base64="rxkqiztuvkmhg79owu1i0qck5qy=">aaab9hicbzdlssnafizp6q3ww9wvuakwwvvj3frcfd24rgavkiyymzy0qyetodmplnc3eny4umstd+pot3f6wwjrdwmf/zmhc+ypus6udpxvq7c2vrg5vdwu7ezu7r+ud49akskkxszneci7avhimccmzppjj5vi4objoxjetuvteurfevggxyn6meklfjfktlh8bizcliekfpnjr1xxqs5m9iq4c6jur0+epf4jjv75qxsmnitramqjup7rpnrpidsmcpyuupnclnah6annujaylz/pjp7y58yj7sir5gltz9zfezmjlrrhgemmir6o5dru/k/mztq68nmm0kyjopnfucztndjtboyqsasajw0qkpm51aydyilqjqesccfd/viqtc6rruf7k8ynzfweuzidc3chbnw4gwy0gcijpmmrvfkj68v6tz7mrqvrmxmmf2r9/gcruptt</latexit> <latexit sha1_base64="kj9jfobhdowigzs4bbhqrpujgrg=">aaab9hicbzbns8naeiyn9avwr6phl4tf8fqsl3osevfywx5ag8pmm2mxbjzxd1moob/diwdfvppjvplv3ly5aoslcw/vzdczb5akro3rfjuljc2t7z3ybmvv/+dwqhp80tzjphi2wcis1q2orseltgw3arupqhohajvb+g5e70xqaz7irznn0y/pupkim2qs5fczgaikfgwyzwbvmlt3fylr4bvqg0lnqfwrhyysi1eajqjwpc9njz9tztgtokv0m40pzwm6xj5fswpufr44ekyurboskfh2sumw7u+jnmzat+padsbujprqbw7+v+tljrrxcy7tzkbky0vrjohjydwbenkfziipbcout7csnqi2amnzqtgqvnuvr0p7qu5zfnbrjdsijjkcwtlcggfx0ib7aeilgdzbm7zcmznxxpx352pzwnkkmvp4i+fzb0cgkmc=</latexit> L 4 g 3 Start with large positive Λ 4, Slowly rolling φ Inflating universe, slowly changing vacuum energy Vacuum energy gets very small, Universe very cold Φ {z} {z} Φ 10 40 yr 10 10 yr Vacuum energy eventually zero - universe crunches, gets hot Key Point: Make Universe Bounce - get hot universe with small vacuum energy

Outline 1. Why? 2. Model 3. Bouncing Universe? 4. Experimental Tests? 5. Conclusions

Why?

<latexit sha1_base64="84uchefsrotfvlevemlx21i3v/m=">aaacbnicbvc7sgnbfl0bxzg+vi1fgaycvdgvqtudnhypipghznc4ozubdjl9mdmrhcwvjb9iy6gird9g56fyozuk0mqda4dz7r1z7/eszqsyrc+jslc4tlxsxc2trw9sbpnbo00zp4lqbol5lnoelpszidyuu5y2e0fx6hha8gaxud+6p0kyolprw4s6ie5flgaeky11zx0nxkppmm9qi+tinjfuiaemb/j49qrrlq2knqaaj/aulm+/g+aoaopd89pxy5kgnfkeyyk7tpuon8ncmclpqoskkiaydhcpdjsnceilm43pgkfdrfgoiiv+kujj9xdhhkmph6gnk/ol5ayxi/95nvqfz27goirvncktj4kuixwjpbpkm0gj4knnmbfm74pihwtmle6upeowz0+ej83jiq35tvwuxsaerdidazgcg06hcldqhwyqeianeifx49f4nt6m90lpwzj27mifgb8/gf2bfg==</latexit> <latexit sha1_base64="y6cbxvuek2fbsomesrrgijxh+mu=">aaacbnicbvdlssnafj3uv62vqesrbovgqiqi6m6igxddvlapagkztcbt0mmdmruhhk7c+ctuxcji1m9w56e4c5k60nyda4dz7r1z7/eswrvy1qdrwlhcwl4pr1bw1jc2t8ztnbaku0lzi8yill2pkcz4xfraqbbuihkjpce63ugy9zt3tcoerzcwtpgbkkhea04jaklv7jshgselimtmskpsrdhatkmp8mntsd+swjwraj4n9g+pnn8fbzp988pxy5qglaiqifi920razygetgwbvjxusytqermwnqyrczlys+kmct7uio+dwooxas7u3x0zczuah56uzjdws14u/uf1ugjo3ixhsqosotopglrgihgecfa5zbtewbncjde7yjokkldqyvv0cpbsyfokfvyznb+2qvulneuz7aeddirsdirq6ao1uqtrdi8e0tn6mr6mj+pvejuwloyfnl30b8b7n7line4=</latexit> <latexit sha1_base64="y6cbxvuek2fbsomesrrgijxh+mu=">aaacbnicbvdlssnafj3uv62vqesrbovgqiqi6m6igxddvlapagkztcbt0mmdmruhhk7c+ctuxcji1m9w56e4c5k60nyda4dz7r1z7/eswrvy1qdrwlhcwl4pr1bw1jc2t8ztnbaku0lzi8yill2pkcz4xfraqbbuihkjpce63ugy9zt3tcoerzcwtpgbkkhea04jaklv7jshgselimtmskpsrdhatkmp8mntsd+swjwraj4n9g+pnn8fbzp988pxy5qglaiqifi920razygetgwbvjxusytqermwnqyrczlys+kmct7uio+dwooxas7u3x0zczuah56uzjdws14u/uf1ugjo3ixhsqosotopglrgihgecfa5zbtewbncjde7yjokkldqyvv0cpbsyfokfvyznb+2qvulneuz7aeddirsdirq6ao1uqtrdi8e0tn6mr6mj+pvejuwloyfnl30b8b7n7line4=</latexit> <latexit sha1_base64="xomc2amwyj1g9fh2xedhqhwhhqy=">aaacbnicbvdlssnafj34rpuvdsncybfcluqexrbduoiign1ae8tkctmonuzczeqooss3/oobf4q49rvc+tdo2i609cda4zx779x7gpqzpr3n21paxlldwy9tlde3tnd27b39lkoysafje57itkauccagqznm0eklkdjg0a6g14xffgcpwclu9cgfpyz9wsjgitzszz7yyqihlpc8psaeylifgnt1myak9+c9u+junqnwinfnpijmaptsly9mabad0jqtpbquk2o/j1izymfc9jifkafd0oeuoyleopx8csyynxglxfeizrmat9tfhtmjlrrfgaksllbzxih+53uzhv36ornppkhq6udrxrfocjejdpkeqvnieeilm7tioicsug2sk5sq3pmtf0nrrooafutualezoeroeb2ju+sic1rdn6ibmoiir/smxtgb9ws9wo/wx7r0yzr1hka/sd5/anyomli=</latexit> Cancellation of Λ L 4 Want to set to zero. How to sense? Key Point: Vacuum energy only couples through Gravity Universal Gravitation Gravity senses total energy in the universe, cannot distinguish individual components Hot early universe? Gravity cannot sense Λ alone Need Λ domination i.e. inflation

<latexit sha1_base64="ozjshu7s47hznkliap4eupyctra=">aaacexicbvc7tsmwfhv4lvikmljyvehdqbkobgmfc0ohitgh1ksv47itvcexbaepivollpwkcwmisbkx8tc4bqzoozklo3puvb73bijrpr3n21pzxvvf2cxsfbd3dvf27ypdlootiuktxyywnqapwigntu01ix0hcyocrtrb+cbz2w9ekhrzez0rxi/qknmbxugbqw+xvqjpeuysru+hpxkhiize3qwiua8kz+cwdwe9maj9u+runbngmnfzugi5gn37ywtjnesea8yqul3xedppkdqumziteokiauexgpkuorxfrpnp7kippdvkcaexni9rofn/d6qoumosbayy218tepn4n9dn9odktykxisyczz8ajazqggbxwjbkgjwbgikwpgzxiediiqxnieutgrt48jjpnvdcw++qpdp1hkcbhimtuayuuaq1casaoakweatp4bw8wu/wi/vufcxlv6y85wj8gfx5a7yiney=</latexit> <latexit sha1_base64="ozjshu7s47hznkliap4eupyctra=">aaacexicbvc7tsmwfhv4lvikmljyvehdqbkobgmfc0ohitgh1ksv47itvcexbaepivollpwkcwmisbkx8tc4bqzoozklo3puvb73bijrpr3n21pzxvvf2cxsfbd3dvf27ypdlootiuktxyywnqapwigntu01ix0hcyocrtrb+cbz2w9ekhrzez0rxi/qknmbxugbqw+xvqjpeuysru+hpxkhiize3qwiua8kz+cwdwe9maj9u+runbngmnfzugi5gn37ywtjnesea8yqul3xedppkdqumziteokiauexgpkuorxfrpnp7kippdvkcaexni9rofn/d6qoumosbayy218tepn4n9dn9odktykxisyczz8ajazqggbxwjbkgjwbgikwpgzxiediiqxnieutgrt48jjpnvdcw++qpdp1hkcbhimtuayuuaq1casaoakweatp4bw8wu/wi/vufcxlv6y85wj8gfx5a7yiney=</latexit> <latexit sha1_base64="ozjshu7s47hznkliap4eupyctra=">aaacexicbvc7tsmwfhv4lvikmljyvehdqbkobgmfc0ohitgh1ksv47itvcexbaepivollpwkcwmisbkx8tc4bqzoozklo3puvb73bijrpr3n21pzxvvf2cxsfbd3dvf27ypdlootiuktxyywnqapwigntu01ix0hcyocrtrb+cbz2w9ekhrzez0rxi/qknmbxugbqw+xvqjpeuysru+hpxkhiize3qwiua8kz+cwdwe9maj9u+runbngmnfzugi5gn37ywtjnesea8yqul3xedppkdqumziteokiauexgpkuorxfrpnp7kippdvkcaexni9rofn/d6qoumosbayy218tepn4n9dn9odktykxisyczz8ajazqggbxwjbkgjwbgikwpgzxiediiqxnieutgrt48jjpnvdcw++qpdp1hkcbhimtuayuuaq1casaoakweatp4bw8wu/wi/vufcxlv6y85wj8gfx5a7yiney=</latexit> <latexit sha1_base64="ozjshu7s47hznkliap4eupyctra=">aaacexicbvc7tsmwfhv4lvikmljyvehdqbkobgmfc0ohitgh1ksv47itvcexbaepivollpwkcwmisbkx8tc4bqzoozklo3puvb73bijrpr3n21pzxvvf2cxsfbd3dvf27ypdlootiuktxyywnqapwigntu01ix0hcyocrtrb+cbz2w9ekhrzez0rxi/qknmbxugbqw+xvqjpeuysru+hpxkhiize3qwiua8kz+cwdwe9maj9u+runbngmnfzugi5gn37ywtjnesea8yqul3xedppkdqumziteokiauexgpkuorxfrpnp7kippdvkcaexni9rofn/d6qoumosbayy218tepn4n9dn9odktykxisyczz8ajazqggbxwjbkgjwbgikwpgzxiediiqxnieutgrt48jjpnvdcw++qpdp1hkcbhimtuayuuaq1casaoakweatp4bw8wu/wi/vufcxlv6y85wj8gfx5a7yiney=</latexit> Bounce? V<latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> L 4 g 3 Inflation, vacuum energy slowly decreases Need to reduce vacuum energy to ~ 10-12 ev 4 Φ Other energy densities (e.g. radiation), smaller than 10-12 ev 4 10 10 years ago, universe had radiation with density 10 24 ev 4 Need to reheat cold empty universe Key Point: Energy not conserved in gravity! Reheat with a bounce!

Capabilities L + g 3 +... Φ rolls, tunes cosmological constant in empty universe. Reheat with a bounce. Weinberg? V,V 0 u 0 Relaxion = Large Number of Minima Phase Transitions? Reheating => hot universe, vacuum energy goes up Sub-dominant. Expand, cool, return to tuned value Bounce + Tuning? Hot universe => Φ rolls. Λeff changes Small change - tuning >> bounce Likely leads to changing Λeff

Model

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sha1_base64="/qxagtb6t8buabslaxmcmdabcku=">aaacdhicbvdlsgmxfm34rpvvdekmwarxzaaw1qxoxo1qwvahu0smvdmgmzmhusowor/gxl9x40irt36ao//gtbbu6oha4zxzubknufiydn0pz2z2bn5hmbeux15zxvsvbgw2tzjqdg2eyerfbsyafde0ukces6wbrygei+d6eorf3ia2ionpcacghbfelelbgvqpuyj2rvbpasdtckh9ccywpxrys32ew8wiaa6vkjbllqqvarlco27jheobebnsjbpuo4v3v5vwniiyuwtgtdxxyttjggwxmmz7qqhf+dxrqcvsmevg2tn4mchdtuqxhom2l0y6vn9ozcwyzhafnhkx7jtpbyt+57vsda/amyhvihdzr0vhkikmdnqm7qonhoxaesa1sh+lvm8042j7y9ssvomt/5jmues5je+sujw8mtsri9tkh+wrj9tiitkhddignnyrb/jenp1759f5cv6/ojpozgal/ilz9gnum5t8</latexit> <latexit sha1_base64="/qxagtb6t8buabslaxmcmdabcku=">aaacdhicbvdlsgmxfm34rpvvdekmwarxzaaw1qxoxo1qwvahu0smvdmgmzmhusowor/gxl9x40irt36ao//gtbbu6oha4zxzubknufiydn0pz2z2bn5hmbeux15zxvsvbgw2tzjqdg2eyerfbsyafde0ukces6wbrygei+d6eorf3ia2ionpcacghbfelelbgvqpuyj2rvbpasdtckh9ccywpxrys32ew8wiaa6vkjbllqqvarlco27jheobebnsjbpuo4v3v5vwniiyuwtgtdxxyttjggwxmmz7qqhf+dxrqcvsmevg2tn4mchdtuqxhom2l0y6vn9ozcwyzhafnhkx7jtpbyt+57vsda/amyhvihdzr0vhkikmdnqm7qonhoxaesa1sh+lvm8042j7y9ssvomt/5jmues5je+sujw8mtsri9tkh+wrj9tiitkhddignnyrb/jenp1759f5cv6/ojpozgal/ilz9gnum5t8</latexit> Simplest Model φ L 4 i g 3 + fa F F Let φ roll through 0, no barriers 1. No Eternal Inflation: g ' 2 i /M pl 2. C.C set by Kinetic Energy: g 3 M pl / mev 4 i / mev 2 M pl 1 3 10 MeV Can check story works (reheating, small c.c. change today)

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sha1_base64="+k2wulhl011dbsfkytjuc2jnbi8=">aaaco3icbvbnaxsxfnqmbzo6x0567exebfxkza4b7b5dc6ahbjxsjwavs2i1b20r7qfs24ir+7966z/olzdcekgiueye2v5o4nramjp5g/qmzkxq6lrnztr6k6fpnjaf1168fpx6tx1r+1hnheiw4jnm1dbkgqriyyacjqxzbswjjzyez1/n/slpufpk6q+c5tbo2cqvseamrrtuv3+kvoqym36sgdf+gy1glpbo26u5dewuy9jxyjlf96efqj9prebr+ofw04t7aeks9qipqkzgemvqb7itzl6n3e5st+uu8i94fwmqcv2g/sepml4kkckxtour5+y4nkyh4blkml9oybk/yxmywzqybptylhyv6a5vihpnyp4u6uk9nzas0xqwhhyyytjvq95c/j83kjd+pdyizquelc8figtjmapzimkkfhcum0syv8l+lfips7wgrbtms/bwv35mjtstz215r3un/s9vhzvkhdkhtekrltkn30ifdagnv8gfusrxzm/nr3pt3cxh15wq85y8ghn7b70nrvq=</latexit> <latexit sha1_base64="+k2wulhl011dbsfkytjuc2jnbi8=">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</latexit> Turtles All the Way Higher Cut-off? Need larger slope at top to combat eternal inflation 2 φ2 L 4 2 2 2 M pl 3 2 + 2 f F F φ1 1 2 1 M pl 3 1 + 1 f F F Key Point: φ2 rolls faster at lower c.c. Use friction to raise barrier 2 / M 2 pl 4 1 1 6 No Bounce

Bouncing Universe

Bouncing Cosmology Independently Motivated Singularity not removed by inflation Infinite Past? Why not?

Bouncing Cosmology Generic Requirement? Need converging geodesics to diverge t Collapsing matter, gravity gets stronger Can matter never escape strong gravity? Black Hole Evaporation Key Point: Matter could escape gravitational singularities Singular Bounce likely possible. Non singular bounce??

Bouncing Cosmology Generic Requirement? Need converging geodesics to diverge t Raychaudhuri s Equation dˆ d = 1 2 ˆ 2 2ˆ2 +2ˆ! 2 T µ U µ U Divergence =) dˆ d > 0 T µ U µ U < 0 or ˆ! 6= 0 Null Energy Violation Vorticity

Vorticity dˆ d = 1 2 ˆ 2 2ˆ2 +2ˆ! 2 T µ U µ U Combat attractive gravity with centrifugal motion Why not use this term? To avoid Null Energy violation, need global vorticity

Godel Universe ds 2 = 2! 2 dt 2 + dr 2 + dy 2 sinh 4 r sinh 2 r d 2 2 p 2 sinh 2 rd dt Cosmological Constant + Spinning Dust Static Universe: Gravity balanced by rotation Closed time-like curves for r > 1 Does not describe region of space-time where we live

The Born Again Universe Have vorticity everywhere, without closed time-like curves? Distant points rotate -> Closed time-like curve To avoid singularity, just need rotation everywhere Key Point: Rotate into compact extra-dimensions? Space-Time: R 4 x T 3 Non-singular bounce without closed time-like curves?

The Metric Space-Time: R 4 X T 3 ds 2 = dt 2 + a (t) 2 d~x 2 + b 2 d 2 + d 2 1 + d 2 2 2 b (sin dtd 1 + cos dtd 2 ) Standard Vorticity Geodesics along R4 forced to move into extra-dimensions Plug in for a(t), use Einstein s Equations to get stress-tensor Can the required stress-tensor be made? 4D effective field theory?

The Stress Tensor ds 2 = dt 2 + a (t) 2 d~x 2 + b 2 d 2 + d 2 1 + d 2 2 2 b (sin dtd 1 + cos dtd 2 ) T tt = M 5 7 3 2 a 00 (t) a(t) + 3 2 1 a 0 (t) 2 3 2 a(t) 2 4b 2! T xx = T yy = T zz = M 5 7 2 2 1 a(t)a 00 (t) 2 1 a 0 (t) 2 + 2 a(t) 2 4b 2 Consider 4D geodesic during bounce. Null Energy? T tt + T xx a (t) 2 2 2b 2 2ä a Vorticity combats gravity, for weak bounce

The Stress Tensor ds 2 = dt 2 + a (t) 2 d~x 2 + b 2 d 2 + d 2 1 + d 2 2 2 b (sin dtd 1 + cos dtd 2 ) Null Energy Condition not violated for 4D geodesics Violated for geodesics into extra-dimensions But can use Casimir! T µ = T C + T M Have Proven: TM preserves dominant energy condition Don t know: Microphysics of TM

The Loophole dˆ d = 1 2 ˆ 2 2ˆ2 +2ˆ! 2 T µ U µ U ds 2 = dt 2 + a (t) 2 d~x 2 + b 2 d 2 + d 2 1 + d 2 2 2 b (sin dtd 1 + cos dtd 2 ) T µ = T C + T M Null Energy Condition in extra-dimensions 4D geodesics carry vorticity into extra-dimensions, avoiding focusing. Need T 3. Metric clearly globally hyperbolic 4D effective field theory?

The Effective Theory ds 2 = dt 2 + a (t) 2 d~x 2 + b 2 d 2 + d 2 1 + d 2 2 2 b (sin dtd 1 + cos dtd 2 ) T tt = M 5 7 3 2 a 00 (t) a(t) + 3 2 1 a 0 (t) 2 3 2 a(t) 2 4b 2! T xx = T yy = T zz = M 5 7 2 2 1 a(t)a 00 (t) 2 1 a 0 (t) 2 + 2 a(t) 2 4b 2 Vorticity terms contribute like a null-energy violating term Can Show: In 4D, KK modes of source + gravivector violate NEC!

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sha1_base64="db8oqbelq4xpwmvl82ehsvde8vs=">aaacpnicbzbnswmxeiazftb6vfxojvgeqsi7iuix6kxeqwx7ad1asmnahmazizkvytjf5sxf4m2jfw+kepvotl2hvgdcxp6zywbeqaluwhwfnbn5hcwl5dxkfnvtfwozslvdm1gskavsses6erddbjeschweayjnsbgivg8gf2m+fs+04zg8hafirzd0jo9ysscidqhqhwt6lijkeor9eyvdapukaobetbm/jc1wft7n5a87xgdzydxd5d/eficc0y4u3zi7dvxxejkooiwq7ckt7anxycrqqyxpeq6cvpkopikn8n5smcj0qhqsaaukitotzhz+co9b0shdsnsnay/pdedcqmogywar02pnbc6f/+wamxrpwwmxkgym6wrqnxyyipx6ittcmwpiaawhmttdme0ttshyx/pwbg/25l+idltyrl45lpbpmztyabftoqpkornurpeogqqiogf0gt7qu/povdofzuekdm7jenbqr3c+vgf/eq/o</latexit> <latexit sha1_base64="db8oqbelq4xpwmvl82ehsvde8vs=">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</latexit> 4D NEC Violation L (@ µ ) 2 + f (@ µ )+V ( ) T µ = @ µ @ + @f @@ µ @ + g µ L Need minus signs. Ghosts/Causality No contribution to NEC. V irrelevant Lorentz Violation L @ µ @ + A µ J µ +... Background vector allows new possibilities UV complete to Lorentz invariant higher dimensional theory

Experimental Tests

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sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> <latexit sha1_base64="0mwspf5svefkuf93elliww/42x8=">aaab6hicbzbns8naeiyn9avwr6phl4tf8fqseeqx6mvjc/yd2la220m7drmjuxuhhp4clx4u8epp8ua/cdvmok0vldy8m8poveeiudau++0unja3tneku6w9/ypdo/lxsvvhqwlyyrgivtegggwx2dlccowmcmkucowek7t5vfoesvnypphpgn5er5khnffjrwz7uk64vxchsg5edhxi1riuv/rdmkurssme1brnuynxm6omzwjnpx6qmafsqkfysyhphnrpfovoyiv1hismlx3skix7eykjkdbtklcdetvjvvqbm//veqkjb/ymyyq1knnyozavxmrkfjuzcoxmikkfyhs3uxi2pooyy7mp2rc81zpxox1v9sw3ryv12zyoipzbovycbzwowz00oaumej7hfd6cr+ffexc+lq0fj585ht9ypn8asrom2g==</latexit> Dark Energy L 4 g 3 Slowly rolling φ, changing dark energy w = 2 V 2 + V Φ Cosmological measurements of the equation of state of dark energy Can φ couple to the standard model? Laboratory measurements of the Dark Energy?

Direct Detection of Dark Energy How can φ interact, while still having a small slope? Axion-like interactions! <latexit sha1_base64="a2q0bm3njqlth/nanramhrgndwe=">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</latexit> sha1_base64="cehuoactk6izcybrr4tl2tykdom=">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</latexit> sha1_base64="ye+zz7oyrftkph3eobcagtgpasa=">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</latexit> L 4 g 3 + F F + @ µ fa f a µ 5 Rotates polarization of light with dark energy evolution Rotates spins moving against dark energy v CMB Polarization Experiments Axion Dark Matter

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