Gemara

(Beraisa): We do not check by light of the sun or moon or a torch, rather, only with light of a Ner, for it is good for checking.

Question: In what case does the Beraisa forbid checking by sunlight?

Answer #1: It forbids checking an Achsadra (a room open on one side).

Rejection: Rava permits checking an Achsadra through its light (i.e. sunlight)!

Answer #3: It forbids checking a room by sunlight that enters through an Arubah (skylight).

Question: Surely, the part under the skylight is permitted. This is just like an Achsadra!

Answer: It forbids checking the sides.

Rishonim

Rif (4b): An Achsadra has great light. One may check it through its light.

Rambam (Hilchos Chametz 2:4): We do not check through sunlight. This refers to holes and hiding places. An Achsadra has great light. If one checked it through sunlight, this suffices.

Magid Mishneh: The Yerushalmi says "the case of checking an Achsadra through sunlight is when he did not check at night." Alternatively, it refers to one who wants to check during the day [of the 13th].

Rosh (1:11): One may check an Achsadra through sunlight, i.e. he was busy and did not check at night, like the Yerushalmi says. This shows that even during the day, one must check [a regular house] with a Ner, even if it has light [through a window].

Ba'al ha'Ma'or (4a): The Beraisa forbids checking through sunlight. Do not say that this is only on the 13th, i.e. because one should [wait to] check on the night of the 14th. Rather, it is forbidden even on the 14th. The Yerushalmi explicitly forbids when he did not check on night of the 14th. On the 14th, he must check with a Ner.

Ran (1a DH v'Ika): Some say that if one wants to check early on the 13th, he may check with a Ner, for even during the day we require light of a Ner. The Beraisa forbids using sunlight. The Yerushalmi says that even if one checks during the day, he must check with light of a Ner. The Beraisa forbids checking through sunlight when he transgressed and did not check on the night of the 14th, or if he wants to check early on the 13th. Also the Ba'al ha'Ma'or says so. This is wrong. The Yerushalmi connotes that one may not check early on the 13th. It asked about checking dark alleys during the day with a Ner, and answered that a Ner does not illuminate during the day like it does at night. Therefore, one may not do so.

Poskim

Shulchan Aruch (OC 433:1): One must check through light of a Ner, and not through moonlight.

Magen Avraham (1): L'Chatchilah one may not check during the day even in a dark house with a Ner.

Chak Yakov (1): If one checked on the night of the 13th, the Bach [and Levush] require checking again. This is wrong. We discuss (4b) one who rented a Dirah b'Chezkas Baduk, and found that it was not checked. This must be on the 13th, for on the 14th surely it is b'Chezkas Baduk! This shows that had Bedikah been done before the 14th, it suffices. It is unreasonable to say that we discuss one who was leaving, who is allowed to check early.

Note: Perhaps also one who will rent his Drishah to others may check early, since he will not be able to check it on the night of the 14th!

Mishnah Berurah (1): Chachamim enacted the Bedikah to be at night, for then light of a Ner enables checking in holes and cracks. If one checked on the day of the 13th with a Ner, he must check again night of the 14th, like Chachamim enacted. In any case, it seems that he does not bless at night, for some Poskim say that he was Yotzei through checking during the day. However, if he checked on the night of the 13th with a Ner, and he was careful not to bring Chametz there afterwards, most Acharonim exempt from checking again. One who wants to be stringent and check again should not bless the latter time.

Note: Based on this, ha'Gaon R. Y. Berkowitz Shlita rules that if one wants Pesach cleaning to count like Bedikah, he closes off the area he cleaned and checks it at night with a Ner. He need not check it again on night of the 14th.

Kaf ha'Chayim (2): If one wants to be stringent and bless, he should use Chametz there before checking.

Shulchan Aruch (ibid.): If one transgressed and did not check on night of the 14th, when he checks on the day of the 14th, he does not check through sunlight, rather, with light of a Ner.

Beis Yosef (DH u'Mah): The Magid Mishneh holds like the Ba'al ha'Ma'or, but the Rosh, Tur and R. Yerucham hold like the Ran. The Tur brings so also from Ra'avan. We hold like them.

Taz (1): The Tur and Beis Yosef discuss one who did not check until the 14th. This implies that checking on the 13th does not help, since Chachamim fixed the Bedikah to be on the night of the 14th. He is like one who checked long before Pesach.

Gra (DH Im): The Shulchan Aruch copied the Rambam's words. The Rosh agrees. This is unlike Rashi and other Poskim, who permit checking l'Chatchilah. There is another reason to require at night, i.e. this is when people are found in their houses.

Shulchan Aruch (ibid.): An Achsadra gets great sunlight. If one checked it through sunlight, this suffices.

Taz (2): L'Chatchilah, one checks the Achsadra on the night of the 14th with a Ner. Rashi and the Rif connote that l'Chatchilah one may check without a Ner during the day. The Bach concludes like the other Poskim, who say that this is only b'Di'eved.

Magen Avraham (2): An Achsadra is on pillars, and has no walls.

Kaf ha'Chayim (6): This is a Roman Achsadra. A Stam Achsadra of the Gemara has three walls (Bava Basra 11b, Tosfos DH Hacha).

Magen Avraham (3): The Gemara says that l'Chatchilah one checks through sunlight. This is when he did not check on the night of the 14th. L'Chatchilah one must check on night of the 14th with a Ner, like it says at the end of this Sa'if. This is why the Shulchan Aruch used an expression of b'Di'eved. There is no argument, like R. Yerucham and the Kesef Mishneh say, unlike the Bach.

Eshel Avraham: The Bach says that there are three opinions. Rashi and the Rif permit checking an Achsadra through sunlight on the day of the 13th. The Rambam requires a Ner l'Chatchilah, even on the 14th. The Rosh and R. Yerucham permit through sunlight on the 14th. The Magen Avraham can explain the Rif like the Rambam, and the Rosh and R. Yerucham agree that l'Chatchilah one may not wait for the day of the 14th. How can he say that Rashi does not argue? Perhaps he agrees that one must leave a room to check on the night of the 14th. This is difficult.

Machatzis ha'Shekel: The Magen Avraham means that all agree that on the night of the 14th, one may not wait to check an Achsadra during the day.

Kaf ha'Chayim (7): R. Zalman says that on the 14th one may check [through daylight] even if it is cloudy.

Kaf ha'Chayim (8): The Bach and R. Zalman say that if a house has many windows and much light, it is like an Achsadra. This is unlike Bigdei Yesha in the name of R. Yerucham. Even if one needs to check only an Achsadra, or there is no Ner, he blesses. One cannot bless for a regular house without a Ner, for he does not do the Mitzvah properly!

Mishnah Berurah (4): An Achsadra is a place with three walls and a roof, and much light through the fourth side, which is totally open.

Mishnah Berurah (5): If one did not check at night, he checks in the morning, for zealous people do Mitzvos promptly. He may not eat before checking.

Mishnah Berurah (6): If one checked during the day of the 13th through sunlight, it seems that he need not check again at night. The Magen Avraham (20) says that he should check at least one room at night.

Shulchan Aruch (ibid.): The same applies to a skylight in a room.

Beis Yosef (DH u'Mihu): R. Yerucham says that checking through its own light helps only for an Achsadra, but not for another house, even if it has much light. He learned from the Gemara's words about a skylight in a room, but did not explain enough. He should have said that this is only regarding the sides, but one may check the middle with light through the skylight.

Magen Avraham (4): Arubah is a window in the roof. This is why R. Yerucham forbids checking through light of a Chalon, i.e. a window in the wall. However, the Tur permits even through a Chalon, and the Rambam connotes like this. Shiltei ha'Giborim says "similarly one may check holes and cracks opposite the Arubah with daylight." This connotes even if the sun is not shining. I say that all forbid with light that comes through a glass window.

Kaf ha'Chayim (9): One must open the glass window pane when checking opposite it without a Ner.

Mishnah Berurah (7): The same applies to directly opposite a Chalon. The sides are like a window with glass. (One must check with a Ner.)