It is brought down in Shulchan Aruch that one is forbidden to talk between Baruch sheAmar and the end of Shemoneh Esrei. In Orach Chaim 51:4.
צריך ליזהר מלהפסיק בדבור משיתחיל ברוך שאמר עד סוף י"ח
This timespan, from Baruch sheAmar until the end of Shemoneh Esrei, presumably includes the time between Yishtabach and Yotzer Or as well. In Orach Chaim 54:3, this is made more explicit:
המספר בין ישתבח ליוצר אור עבירה היא בידו וחוזר עליה מעורכי המלחמה ויש מי שאומר שלצרכי ציבור או לפסוק צדקה למי שבא חהתפרנס מן הצדקה מותר להפסיק
What is the source of this prohibition? A prohibition on talking within Pesukei deZimra (except for greeting and responding to greetings in certain instances) is understandable -- since Baruch sheAmar and Yishtabach were instituted as bracketing blessings, this is an instance of beracha hasemucha lachaverta, and so one should not interrupt. However, Yishtabach is the end of one section of prayer -- pesukei deZimra, and Yotzer Or is the beginning of another section. Why should a prohibition on speech exist at this point in the prayers?
There are two primary sources for prohibiting speech at this point. One source -- that for Orach Chaim 51:4 -- is the Rif who prohibits speech from Baruch sheAmar until the end of Shemoneh Esrei. The second source -- that for Orach Chaim 54:3 -- is the Yerushalmi that states that if one talks between Yishtabach and Yotzer Or, he has a sin in hand and would be turned back from the Jewish army for certain wars for that sin. The difficulty with this Yerushalmi is that it does not exist and cannot exist, as I will eventually explain. Now, it is quite possible that Rif's basis is this Yerushalmi, but we shall consider each source in turn.
Rif
The Rif (on daf 23 in Brachot in pages of Rif) writes:
וגרסינן בפרק כל כתבי הקדש אמר רבי יוסי יהא חלקי עם גומרי הלל בכל יום. איני והאמר מר הקורא הלל בכל יום הרי זה מחרף ומגדף. כי קא אמרינן בפסוקי דזמרה אמרינן.
מאי ניהו מתהלה לדוד עד כל הנשמה תהלל יה. ותקנו רבנן למימר ברכה מקמייהו וברכה מבתרייהו ומאי ניהו ברוך שאמר וישתבח. הלכך מיבעיה ליה לאיניש דלא לאשתעויי מכי מתחיל בברוך שאמר עד דמסיים [ליה] לשמונה עשרה
מאי ניהו מתהלה לדוד עד כל הנשמה תהלל יה. ותקנו רבנן למימר ברכה מקמייהו וברכה מבתרייהו ומאי ניהו ברוך שאמר וישתבח. הלכך מיבעיה ליה לאיניש דלא לאשתעויי מכי מתחיל בברוך שאמר עד דמסיים [ליה] לשמונה עשרה
This is somewhat surprising. After all, Rif mentions the bracketing blessings before and after - baruch sheAmar and Yishtabach. The conclusion we would expect would be that therefore one should not speak from the time that he begins Baruch sheAmar until he finishes Yishtabach, not until he finishes Shemoneh Esrei!
One can make sense of most of this prohibition. After all, the reading of Shema also has blessings before and after it, which would make it prohibited for one to speak from the blessing of Yotzer Or until Ga'al Yisrael. And the statement that teikef lig`ula tefillah is taken by many to mean a prohibition of interrupting between the final blessing of Shema and the beginning of Shemoneh Esrei not only by waiting between but also of speaking between. (See Midrash Rabba on parshat vaEtchanan where it is taken to mean waiting rather than speaking.) And within the silent Shemoneh Esrei, of course one cannot talk. The only gap in this span is between Yishtabach and Yotzer Or, and perhaps the Rif was relying on the aforementioned Yerushalmi to prohibit this gap as well.
There are three approaches we can take to this difficult Rif. We can say that the Rif said it and meant it. We can say that the Rif said it and didn't mean it. Or, we can say that the Rif didn't say it.
The traditional approach is that the Rif said it and meant it. Some who take this approach are Rabbenu Yonah, Shiltei haGiborim, and Hagahot Maimoni.
Rabbenu Yonah (ד"ה ותקינו) writes:
וכיון שתקנו ברכה עליהם אין לו לשוח בהם ובמדרש אומר שאפילו בין ברכת ישתבח ליוצר אור אין לו להפסיק כלל וכן כתב הרב אלפסי ז"ל
thus explaining Rif on the basis of a midrash. This "midrash" is presumably the Yerushalmi.
Shiltei haGiborim writes (note ד):
וכן יש בירושלמי הסח בין ישתבח ליוצר אור עבירה היא בידו וחוזרין אותו ממערכי המלחמה
thus explaining the Rif on the basis of the Yerushalmi.
Rambam mentions no such prohibition in the 7th perek of hilchot tefillah, but there, Hagahot Maimoni writes:
וברוך שאמר וישתבח הוי כמו ברכה הסמוכה לחבירתה. ובדברי גאון כתוב אסור לאישתעויי בין ברוך שאמר עד שיחתם בישתבח מספר אבי"ה.
וגרסינן בירושלמי המספר בין ישתבח ליוצר אור עבירה היא בידו וחוזר עליה ממערכי המלחמה. ולכך נהגו לומר ישתבח מעומד כמו יוצר שהרי אסור להפסיק וכן רשי אסר להפסיק וכן באלפס כתב דלא מיבעי' ליה לאשתעויי מכי מתחיל בברוך שאמר עד מסיים ליה י"ח ע"כ
וגרסינן בירושלמי המספר בין ישתבח ליוצר אור עבירה היא בידו וחוזר עליה ממערכי המלחמה. ולכך נהגו לומר ישתבח מעומד כמו יוצר שהרי אסור להפסיק וכן רשי אסר להפסיק וכן באלפס כתב דלא מיבעי' ליה לאשתעויי מכי מתחיל בברוך שאמר עד מסיים ליה י"ח ע"כ
Thus he cites a Gaon that only prohibits until the end of Yishtabach, but then cites the same Yerushalmi that prohibits talking between Yishtabach and Yotzer Or, finally noting Rif also prohibits.
It is strange, however, that Rif does not cite this Yerushalmi explicitly, if he is indeed relying upon it for determining halacha. Indeed, Rif does not shy away from citing Yerushalmis as appropriate. That he does not mention this critical Yerushalmi before making the leap to prohibit the entire timespan is a bit suspicious.
The second approach one could take is thus that Rif said it but didn't mean it. He wrote that one is prohibited from talking from Baruch sheAmar until he finishes Shemoneh Esrei but meant only most of that timespan - because of the blessing of Shema and the importance of following the final blessing of Shema immediately by Shemoneh Esrei. That there is one gap in the middle, between Yishtabach and Yotzer Or, in which one can talk is immaterial to Rif's main point - that for the vast majority of tefillah, one is now prohibited from talking. But Rif would agree that, at this particular point, one can talk.
The third approach one could take is that the Rif never said it. That is, what we have in the Rif is a scribal error and he only meant to prohibit until one finishes Yishtabach, not until one finished Shemoneh Esrei. This would also account for the fact that Rif does not cite the Yerushalmi -- he never meant to prohibit between Yishtabach and Yotzer Or.
The Hagaot Maimoni is invaluable to arguing for this approach. Firstly, he cites the words of a Goan: